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W2010618448 abstract "Let <svg style=vertical-align:-0.0pt;width:13.3125px; id=M1 height=11.175 version=1.1 viewBox=0 0 13.3125 11.175 width=13.3125 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,11.113)><path id=x1D43E d=M764 650l-7 -26q-61 -10 -91.5 -22.5t-76.5 -48.5l-235 -184q104 -152 208 -276q31 -37 54.5 -48.5t68.5 -16.5l-7 -28h-156q-138 170 -213 284q-19 29 -33.5 35t-33.5 -7l-29 -173q-15 -75 -5.5 -90.5t74.5 -20.5l-5 -28h-260l7 28q58 5 74 21.5t30 89.5l70 378
q12 68 2 83t-72 22l6 28h257l-7 -28q-62 -7 -76 -21.5t-27 -83.5l-32 -172q29 11 78 46q112 84 217 179q18 16 23.5 25.5t-1 14.5t-26.5 8l-30 4l5 28h249z /></g> </svg> be a nonempty, closed, and convex subset of a real uniformly convex Banach space <svg style=vertical-align:-0.0pt;width:10.8625px; id=M2 height=11.175 version=1.1 viewBox=0 0 10.8625 11.175 width=10.8625 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,11.113)><path id=x1D438 d=M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5
l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z /></g> </svg>. Let <svg style=vertical-align:-3.3907pt;width:52.075001px; id=M3 height=16.4 version=1.1 viewBox=0 0 52.075001 16.4 width=52.075001 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><path id=x7B d=M293 -169q-145 0 -145 128q0 35 4 106t3 104q0 17 -2 28t-10 25.5t-28 23t-51 10.5v29q31 2 51 10.5t28 23t10 25.5t2 28q0 31 -4 101t-3 104q0 132 145 132v-28q-51 -7 -67.5 -30t-16.5 -63q0 -32 6.5 -99.5t6.5 -100.5q0 -97 -83 -115v-4q83 -20 83 -117
q0 -34 -6.5 -99.5t-6.5 -96.5q0 -41 16.5 -65.5t67.5 -31.5v-28z /></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><path id=x1D447 d=M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z /></g> <g transform=matrix(.012,-0,0,-.012,17.287,16.2)><path id=x1D706 d=M529 97q-70 -109 -136 -109q-41 0 -56 94q-23 144 -37 284q-38 -88 -99 -202.5t-93 -156.5q-26 -8 -76 -19l-9 21q71 78 145.5 193t124.5 232q-5 84 -15 128q-12 55 -29.5 75.5t-42.5 20.5q-21 0 -45 -13l-8 24q16 17 46 30t55 13q43 0 70 -46.5t40 -169.5
q27 -249 51 -392q7 -46 23 -46q24 0 70 60z /></g> <g transform=matrix(.017,-0,0,-.017,24.475,12.112)><path id=x7D d=M283 255q-31 -2 -51 -10.5t-28 -23.5t-10 -27t-2 -30q0 -28 4 -97.5t4 -107.5q0 -128 -146 -128v28q50 7 67.5 31t17.5 63q0 33 -7 100t-7 98q0 96 84 117v4q-84 20 -84 115q0 34 7 102.5t7 98.5q0 40 -17.5 63t-67.5 30v28q28 0 50 -4t45.5 -16.5t37 -40t13.5 -68.5
q0 -37 -4 -106.5t-4 -98.5q0 -18 2 -30t10 -27t28 -23.5t51 -10.5v-29z /></g> <g transform=matrix(.012,-0,0,-.012,30.375,16.2)><use xlink:href=#x1D706/></g><g transform=matrix(.012,-0,0,-.012,36.943,16.2)><path id=x2208 d=M448 1h-83q-118 0 -201.5 74.5t-83.5 179.5t83.5 179.5t201.5 74.5h83v-50h-84q-87 0 -150.5 -51.5t-73.5 -127.5h308v-50h-308q10 -76 73.5 -127.5t150.5 -51.5h84v-50z /></g><g transform=matrix(.012,-0,0,-.012,43.226,16.2)><path id=x39B d=M671 0h-247v28q49 7 60 18.5t0 45.5l-155 438h-2q-21 -61 -74 -204.5t-75 -210.5q-15 -51 -4.5 -65t67.5 -22v-28h-221v28q50 9 69 26.5t45 84.5l202 517l32 9l194 -535q23 -61 42 -78.5t67 -23.5v-28z /></g> </svg> and <svg style=vertical-align:-3.3907pt;width:48.912498px; id=M4 height=16.4 version=1.1 viewBox=0 0 48.912498 16.4 width=48.912498 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><path id=x1D446 d=M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68
l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z /></g> <g transform=matrix(.012,-0,0,-.012,14.125,16.2)><use xlink:href=#x1D706/></g> <g transform=matrix(.017,-0,0,-.017,21.312,12.112)><use xlink:href=#x7D/></g> <g transform=matrix(.012,-0,0,-.012,27.213,16.2)><use xlink:href=#x1D706/></g><g transform=matrix(.012,-0,0,-.012,33.781,16.2)><use xlink:href=#x2208/></g><g transform=matrix(.012,-0,0,-.012,40.063,16.2)><use xlink:href=#x39B/></g> </svg> be two infinite families of asymptotically nonexpansive mappings from <svg style=vertical-align:-0.0pt;width:13.3125px; id=M5 height=11.175 version=1.1 viewBox=0 0 13.3125 11.175 width=13.3125 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,11.113)><use xlink:href=#x1D43E/></g> </svg> to itself with <svg style=vertical-align:-3.3907pt;width:280.71249px; id=M6 height=16.450001 version=1.1 viewBox=0 0 280.71249 16.450001 width=280.71249 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.162)><path id=x1D439 d=M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z /></g><g transform=matrix(.017,-0,0,-.017,15.344,12.162)><path id=x2236 d=M223 355q0 -25 -15.5 -41.5t-39.5 -16.5t-40 16.5t-16 41.5t16 41t40 16t39.5 -16t15.5 -41zM223 46q0 -26 -16 -42t-40 -16t-39.5 16t-15.5 42q0 24 16 40.5t39 16.5q24 0 40 -16.5t16 -40.5z /></g><g transform=matrix(.017,-0,0,-.017,21.022,12.162)><path id=x3D d=M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z /></g><g transform=matrix(.017,-0,0,-.017,35.726,12.162)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,41.624,12.162)><path id=x1D465 d=M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z /></g><g transform=matrix(.017,-0,0,-.017,55.852,12.162)><use xlink:href=#x2208/></g><g transform=matrix(.017,-0,0,-.017,69.553,12.162)><use xlink:href=#x1D43E/></g><g transform=matrix(.017,-0,0,-.017,87.453,12.162)><use xlink:href=#x2236/></g><g transform=matrix(.017,-0,0,-.017,97.856,12.162)><use xlink:href=#x1D447/></g> <g transform=matrix(.012,-0,0,-.012,109.188,16.25)><use xlink:href=#x1D706/></g> <g transform=matrix(.017,-0,0,-.017,116.375,12.162)><use xlink:href=#x1D465/></g><g transform=matrix(.017,-0,0,-.017,130.603,12.162)><use xlink:href=#x3D/></g><g transform=matrix(.017,-0,0,-.017,145.29,12.162)><use xlink:href=#x1D465/></g><g transform=matrix(.017,-0,0,-.017,159.518,12.162)><use xlink:href=#x3D/></g><g transform=matrix(.017,-0,0,-.017,174.222,12.162)><use xlink:href=#x1D446/></g> <g transform=matrix(.012,-0,0,-.012,182.388,16.25)><use xlink:href=#x1D706/></g> <g transform=matrix(.017,-0,0,-.017,189.575,12.162)><use xlink:href=#x1D465/></g><g transform=matrix(.017,-0,0,-.017,199.077,12.162)><path id=x2C d=M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z /></g><g transform=matrix(.017,-0,0,-.017,205.775,12.162)><use xlink:href=#x1D706/></g><g transform=matrix(.017,-0,0,-.017,219.884,12.162)><use xlink:href=#x2208/></g><g transform=matrix(.017,-0,0,-.017,233.585,12.162)><use xlink:href=#x39B/></g><g transform=matrix(.017,-0,0,-.017,245.246,12.162)><use xlink:href=#x7D/></g><g transform=matrix(.017,-0,0,-.017,253.983,12.162)><path id=x2260 d=M535 138h-247l-72 -237l-55 17l67 220h-176v50h192l41 135h-233v50h248l73 237l54 -17l-67 -220h175v-50h-190l-41 -135h231v-50z /></g><g transform=matrix(.017,-0,0,-.017,266.783,12.162)><path id=x2205 d=M754 617l-97 -96q78 -89 78 -209q0 -134 -96 -228.5t-232 -94.5q-119 0 -211 76l-97 -95l-38 38l96 95q-77 90 -77 209q0 134 95.5 229t231.5 95q121 0 212 -77l97 96zM677 312q0 96 -59 171l-384 -380q75 -64 173 -64q112 0 191 80t79 193zM581 522q-75 64 -174 64
q-112 0 -190.5 -80.5t-78.5 -193.5q0 -94 58 -170z /></g> </svg>. For an arbitrary initial point <svg style=vertical-align:-3.3907pt;width:47.575001px; id=M7 height=15.4 version=1.1 viewBox=0 0 47.575001 15.4 width=47.575001 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,11.112)><use xlink:href=#x1D465/></g> <g transform=matrix(.012,-0,0,-.012,9.563,15.187)><path id=x30 d=M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z /></g> <g transform=matrix(.017,-0,0,-.017,20.625,11.112)><use xlink:href=#x2208/></g><g transform=matrix(.017,-0,0,-.017,34.309,11.112)><use xlink:href=#x1D43E/></g> </svg>, <svg style=vertical-align:-3.3907pt;width:28.025px; id=M8 height=16.4 version=1.1 viewBox=0 0 28.025 16.4 width=28.025 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><use xlink:href=#x1D465/></g> <g transform=matrix(.012,-0,0,-.012,15.462,16.2)><path id=x1D45B d=M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z /></g> <g transform=matrix(.017,-0,0,-.017,22.062,12.112)><use xlink:href=#x7D/></g> </svg> is defined as follows: <svg style=vertical-align:-4.15506pt;width:304.51251px; id=M9 height=18.924999 version=1.1 viewBox=0 0 304.51251 18.924999 width=304.51251 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,13.688)><use xlink:href=#x1D465/></g> <g transform=matrix(.012,-0,0,-.012,9.563,17.763)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,20.888,13.688)><use xlink:href=#x3D/></g><g transform=matrix(.017,-0,0,-.017,35.574,13.688)><path id=x1D6FC d=M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204
q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z /></g> <g transform=matrix(.012,-0,0,-.012,45.238,17.763)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,51.838,13.688)><use xlink:href=#x1D465/></g> <g transform=matrix(.012,-0,0,-.012,61.338,17.763)><use xlink:href=#x1D45B/></g><g transform=matrix(.012,-0,0,-.012,67.311,17.763)><path id=x2212 d=M535 230h-483v50h483v-50z /></g><g transform=matrix(.012,-0,0,-.012,74.295,17.763)><path id=x31 d=M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z /></g> <g transform=matrix(.017,-0,0,-.017,84.4,13.688)><path id=x2B d=M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z /></g><g transform=matrix(.017,-0,0,-.017,98.152,13.688)><path id=x1D6FD d=M558 587q0 -32 -14 -61t-40 -53.5t-48.5 -41t-54.5 -36.5q144 -51 144 -174q0 -55 -43.5 -108t-104.5 -87q-77 -42 -131 -42q-31 0 -54 20t-31 47l11 18q48 -29 108 -29q79 0 119.5 43t40.5 109t-44.5 107.5t-119.5 50.5l22 47q34 1 65 21q96 61 96 157q0 42 -24 67.5
t-62 25.5q-24 0 -43.5 -9t-35 -29.5t-27 -44t-22.5 -63t-19.5 -75.5t-18.5 -91q-57 -294 -68 -380q-26 -190 -35 -200q-26 -31 -97 -37l-4 26q19 9 48 170l77 413q23 121 52.5 187.5t83.5 114.5q70 62 148 62q51 0 88.5 -34t37.5 -91z /></g> <g transform=matrix(.012,-0,0,-.012,108.038,18.712)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,114.638,13.688)><path id=x28 d=M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z /></g><g transform=matrix(.017,-0,0,-.017,120.519,13.688)><use xlink:href=#x1D447/></g> <g transform=matrix(.012,-0,0,-.012,131.838,5.525)><path id=x2217 d=M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5
q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z /></g><g transform=matrix(.012,-0,0,-.012,131.838,17.763)><use xlink:href=#x1D45B/></g><g transform=matrix(.012,-0,0,-.012,137.811,17.763)><use xlink:href=#x2212/></g><g transform=matrix(.012,-0,0,-.012,144.795,17.763)><use xlink:href=#x31/></g> <g transform=matrix(.017,-0,0,-.017,151.125,13.688)><path id=x29 d=M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z /></g> <g transform=matrix(.012,-0,0,-.012,157.012,5.525)><path id=x1D45A d=M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
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t0.5 -143.5h2q155 193 155 297q0 26 -12 47q-5 8 -5 15q0 16 12.5 27t29.5 11q21 0 34 -21t13 -55z /></g> <g transform=matrix(.012,-0,0,-.012,235.825,18.712)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,242.425,13.688)><use xlink:href=#x28/></g><g transform=matrix(.017,-0,0,-.017,248.307,13.688)><use xlink:href=#x1D447/></g> <g transform=matrix(.012,-0,0,-.012,259.625,5.525)><use xlink:href=#x2217/></g><g transform=matrix(.012,-0,0,-.012,259.625,17.763)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,267.225,13.688)><use xlink:href=#x29/></g> <g transform=matrix(.012,-0,0,-.012,273.112,5.525)><use xlink:href=#x1D45A/></g> <g transform=matrix(.008,-0,0,-.008,282.5,8.375)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,288.012,13.688)><path id=x1D466 d=M556 393q0 -39 -36 -106q-42 -78 -185 -279q-47 -66 -81 -108t-117 -135l-112 -26l-8 22q150 90 251 219q-6 136 -39 340q-8 53 -21 53q-6 0 -27 -19.5t-38 -42.5l-16 26q80 111 127 111q23 0 35 -28t20 -90q18 -137 27 -263h2q142 200 142 279q0 24 -14 48q-4 7 5 26
q13 28 43 28q18 0 30 -15.5t12 -39.5z /></g> <g transform=matrix(.012,-0,0,-.012,297.85,18.712)><use xlink:href=#x1D45B/></g> </svg>, <svg style=vertical-align:-4.15506pt;width:285.48749px; id=M10 height=22.887501 version=1.1 viewBox=0 0 285.48749 22.887501 width=285.48749 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,17.65)><use xlink:href=#x1D466/></g> <g transform=matrix(.012,-0,0,-.012,9.9,22.675)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,21.225,17.65)><use xlink:href=#x3D/></g><g transform=matrix(.017,-0,0,-.017,35.912,17.65)><use xlink:href=#x1D6FC/></g> <g transform=matrix(.012,-0,0,-.012,45.575,9.488)><path id=x2032 d=M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z /></g><g transform=matrix(.012,-0,0,-.012,45.575,21.725)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,52.175,17.65)><use xlink:href=#x1D465/></g> <g transform=matrix(.012,-0,0,-.012,61.675,21.725)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,72.05,17.65)><use xlink:href=#x2B/></g><g transform=matrix(.017,-0,0,-.017,85.802,17.65)><use xlink:href=#x1D6FD/></g> <g transform=matrix(.012,-0,0,-.012,95.688,9.488)><use xlink:href=#x2032/></g><g transform=matrix(.012,-0,0,-.012,95.688,22.675)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,102.275,17.65)><use xlink:href=#x28/></g><g transform=matrix(.017,-0,0,-.017,108.157,17.65)><use xlink:href=#x1D446/></g> <g transform=matrix(.012,-0,0,-.012,116.312,9.488)><use xlink:href=#x2217/></g><g transform=matrix(.012,-0,0,-.012,116.312,21.725)><use xlink:href=#x1D45B/></g><g transform=matrix(.012,-0,0,-.012,122.286,21.725)><use xlink:href=#x2212/></g><g transform=matrix(.012,-0,0,-.012,129.27,21.725)><use xlink:href=#x31/></g> <g transform=matrix(.017,-0,0,-.017,135.612,17.65)><use xlink:href=#x29/></g> <g transform=matrix(.012,-0,0,-.012,141.488,9.488)><use xlink:href=#x1D45A/></g> <g transform=matrix(.008,-0,0,-.008,150.875,12.337)><use xlink:href=#x1D45B/></g><g transform=matrix(.008,-0,0,-.008,155.141,12.337)><use xlink:href=#x2212/></g><g transform=matrix(.008,-0,0,-.008,160.13,12.337)><use xlink:href=#x31/></g> <g transform=matrix(.017,-0,0,-.017,165.462,17.65)><use xlink:href=#x1D465/></g> <g transform=matrix(.012,-0,0,-.012,174.962,21.725)><use xlink:href=#x1D45B/></g><g transform=matrix(.012,-0,0,-.012,180.936,21.725)><use xlink:href=#x2212/></g><g transform=matrix(.012,-0,0,-.012,187.92,21.725)><use xlink:href=#x31/></g> <g transform=matrix(.017,-0,0,-.017,198.038,17.65)><use xlink:href=#x2B/></g><g transform=matrix(.017,-0,0,-.017,211.789,17.65)><use xlink:href=#x1D6FE/></g> <g transform=matrix(.012,-0,0,-.012,220.3,9.488)><use xlink:href=#x2032/></g><g transform=matrix(.012,-0,0,-.012,220.3,22.675)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,226.9,17.65)><use xlink:href=#x28/></g><g transform=matrix(.017,-0,0,-.017,232.782,17.65)><use xlink:href=#x1D446/></g> <g transform=matrix(.012,-0,0,-.012,240.938,9.488)><use xlink:href=#x2217/></g><g transform=matrix(.012,-0,0,-.012,240.938,21.725)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,248.55,17.65)><use xlink:href=#x29/></g> <g transform=matrix(.012,-0,0,-.012,254.438,9.488)><use xlink:href=#x1D45A/></g> <g transform=matrix(.008,-0,0,-.008,263.825,12.337)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,269.338,17.65)><use xlink:href=#x1D465/></g> <g transform=matrix(.012,-0,0,-.012,278.838,21.725)><use xlink:href=#x1D45B/></g> </svg>, <svg style=vertical-align:-1.59705pt;width:92.012497px; id=M11 height=12.9125 version=1.1 viewBox=0 0 92.012497 12.9125 width=92.012497 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,10.862)><use xlink:href=#x1D45B/></g><g transform=matrix(.017,-0,0,-.017,13.305,10.862)><use xlink:href=#x3D/></g><g transform=matrix(.017,-0,0,-.017,28.008,10.862)><use xlink:href=#x31/></g><g transform=matrix(.017,-0,0,-.017,36.168,10.862)><use xlink:href=#x2C/></g><g transform=matrix(.017,-0,0,-.017,42.882,10.862)><path id=x32 d=M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z /></g><g transform=matrix(.017,-0,0,-.017,51.042,10.862)><use xlink:href=#x2C/></g><g transform=matrix(.017,-0,0,-.017,57.739,10.862)><path id=x33 d=M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z /></g><g transform=matrix(.017,-0,0,-.017,65.899,10.862)><use xlink:href=#x2C/></g><g transform=matrix(.017,-0,0,-.017,72.613,10.862)><path id=x2026 d=M160 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16zM485 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16zM806 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5
t16 -40.5q0 -26 -15.5 -42t-41.5 -16z /></g> </svg>, where <svg style=vertical-align:-7.28917pt;width:64.824997px; id=M12 height=22.825001 version=1.1 viewBox=0 0 64.824997 22.825001 width=64.824997 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,13.688)><use xlink:href=#x1D447/></g> <g transform=matrix(.012,-0,0,-.012,11.388,5.525)><use xlink:href=#x2217/></g><g transform=matrix(.012,-0,0,-.012,11.388,17.763)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,23.712,13.688)><use xlink:href=#x3D/></g><g transform=matrix(.017,-0,0,-.017,38.399,13.688)><use xlink:href=#x1D447/></g> <g transform=matrix(.012,-0,0,-.012,49.738,17.763)><use xlink:href=#x1D706/></g> <g transform=matrix(.008,-0,0,-.008,56.3,20.625)><path id=x1D456 d=M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
q16 0 76 48z /></g><g transform=matrix(.008,-0,0,-.008,58.625,22.663)><use xlink:href=#x1D45B/></g> </svg> and <svg style=vertical-align:-7.28917pt;width:58.5px; id=M13 height=22.825001 version=1.1 viewBox=0 0 58.5 22.825001 width=58.5 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,13.688)><use xlink:href=#x1D446/></g> <g transform=matrix(.012,-0,0,-.012,8.225,5.525)><use xlink:href=#x2217/></g><g transform=matrix(.012,-0,0,-.012,8.225,17.763)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,20.55,13.688)><use xlink:href=#x3D/></g><g transform=matrix(.017,-0,0,-.017,35.237,13.688)><use xlink:href=#x1D446/></g> <g transform=matrix(.012,-0,0,-.012,43.412,17.763)><use xlink:href=#x1D706/></g> <g transform=matrix(.008,-0,0,-.008,49.975,20.625)><use xlink:href=#x1D456/></g><g transform=matrix(.008,-0,0,-.008,52.3,22.663)><use xlink:href=#x1D45B/></g> </svg> with <svg style=vertical-align:-3.3907pt;width:11.3625px; id=M14 height=15.4875 version=1.1 viewBox=0 0 11.3625 15.4875 width=11.3625 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,11.2)><use xlink:href=#x1D456/></g> <g transform=matrix(.012,-0,0,-.012,4.7,15.275)><use xlink:href=#x1D45B/></g> </svg> and <svg style=vertical-align:-3.3907pt;width:20.137501px; id=M15 height=11.9625 version=1.1 viewBox=0 0 20.137501 11.9625 width=20.137501 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,7.675)><use xlink:href=#x1D45A/></g> <g transform=matrix(.012,-0,0,-.012,13.475,11.762)><use xlink:href=#x1D45B/></g> </svg> satisfying the positive integer equation: <svg style=vertical-align:-2.3205pt;width:129.7px; id=M16 height=15.0875 version=1.1 viewBox=0 0 129.7 15.0875 width=129.7 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.138)><use xlink:href=#x1D45B/></g><g transform=matrix(.017,-0,0,-.017,13.305,12.138)><use xlink:href=#x3D/></g><g transform=matrix(.017,-0,0,-.017,28.008,12.138)><use xlink:href=#x1D456/></g><g transform=matrix(.017,-0,0,-.017,36.423,12.138)><use xlink:href=#x2B/></g><g transform=matrix(.017,-0,0,-.017,50.175,12.138)><use xlink:href=#x28/></g><g transform=matrix(.017,-0,0,-.017,56.056,12.138)><use xlink:href=#x1D45A/></g><g transform=matrix(.017,-0,0,-.017,73.259,12.138)><use xlink:href=#x2212/></g><g transform=matrix(.017,-0,0,-.017,87.011,12.138)><use xlink:href=#x31/></g><g transform=matrix(.017,-0,0,-.017,95.171,12.138)><use xlink:href=#x29/></g><g transform=matrix(.017,-0,0,-.017,101.052,12.138)><use xlink:href=#x1D45A/></g><g transform=matrix(.017,-0,0,-.017,114.464,12.138)><path id=x2F d=M368 703l-264 -866h-60l265 866h59z /></g><g transform=matrix(.017,-0,0,-.017,121.468,12.138)><use xlink:href=#x32/></g> </svg>, <svg style=vertical-align:-0.546pt;width:37.599998px; id=M17 height=11.9375 version=1.1 viewBox=0 0 37.599998 11.9375 width=37.599998 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,11.2)><use xlink:href=#x1D45A/></g><g transform=matrix(.017,-0,0,-.017,18.183,11.2)><path id=x2265 d=M531 285l-474 -214v56l416 183l-416 184v56l474 -215v-50zM531 -40h-474v50h474v-50z /></g><g transform=matrix(.017,-0,0,-.017,32.887,11.2)><use xlink:href=#x1D456/></g> </svg>; <svg style=vertical-align:-5.65115pt;width:49.950001px; id=M18 height=20.65 version=1.1 viewBox=0 0 49.950001 20.65 width=49.950001 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,13.55)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,13.55)><use xlink:href=#x1D447/></g> <g transform=matrix(.012,-0,0,-.012,17.287,17.637)><use xlink:href=#x1D706/></g> <g transform=matrix(.008,-0,0,-.008,23.85,20.487)><use xlink:href=#x1D456/></g> <g transform=matrix(.017,-0,0,-.017,27.412,13.55)><use xlink:href=#x7D/></g> <g transform=matrix(.012,-0,0,-.012,33.312,5.387)><path id=x221E d=M983 225q0 -112 -67 -174.5t-150 -62.5q-91 0 -154.5 43.5t-113.5 129.5q-49 -85 -104 -129t-138 -44q-98 0 -158.5 66t-60.5 154q0 59 21 106.5t54.5 75.5t70.5 43t73 15q90 0 152.5 -43.5t112.5 -128.5q48 84 104.5 128t140.5 44q93 0 155 -65t62 -158zM478 196
q-27 49 -47 80t-50 67t-64 54t-73 18q-48 0 -81.5 -47t-33.5 -128q0 -96 37.5 -157.5t99.5 -61.5q68 0 117.5 47t94.5 128zM889 204q0 91 -35.5 151t-99.5 60q-68 0 -119 -47t-95 -127q27 -49 47 -80.5t50 -67.5t65 -54t74 -18q113 0 113 183z /></g><g transform=matrix(.012,-0,0,-.012,33.312,17.638)><use xlink:href=#x1D456/></g><g transform=matrix(.012,-0,0,-.012,36.561,17.638)><use xlink:href=#x3D/></g><g transform=matrix(.012,-0,0,-.012,43.545,17.638)><use xlink:href=#x31/></g> </svg> and <svg style=vertical-align:-5.65115pt;width:46.787498px; id=M19 height=20.65 version=1.1 viewBox=0 0 46.787498 20.65 width=46.787498 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,13.55)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,13.55)><use xlink:href=#x1D446/></g> <g transform=matrix(.012,-0,0,-.012,14.125,17.637)><use xlink:href=#x1D706/></g> <g transform=matrix(.008,-0,0,-.008,20.687,20.487)><use xlink:href=#x1D456/></g> <g transform=matrix(.017,-0,0,-.017,24.25,13.55)><use xlink:href=#x7D/></g> <g transform=matrix(.012,-0,0,-.012,30.15,5.387)><use xlink:href=#x221E/></g><g transform=matrix(.012,-0,0,-.012,30.15,17.638)><use xlink:href=#x1D456/></g><g transform=matrix(.012,-0,0,-.012,33.398,17.638)><use xlink:href=#x3D/></g><g transform=matrix(.012,-0,0,-.012,40.383,17.638)><use xlink:href=#x31/></g> </svg> are two countable subsets of <svg style=vertical-align:-3.3907pt;width:52.075001px; id=M20 height=16.4 version=1.1 viewBox=0 0 52.075001 16.4 width=52.075001 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><use xlink:href=#x1D447/></g> <g transform=matrix(.012,-0,0,-.012,17.287,16.2)><use xlink:href=#x1D706/></g> <g transform=matrix(.017,-0,0,-.017,24.475,12.112)><use xlink:href=#x7D/></g> <g transform=matrix(.012,-0,0,-.012,30.375,16.2)><use xlink:href=#x1D706/></g><g transform=matrix(.012,-0,0,-.012,36.943,16.2)><use xlink:href=#x2208/></g><g transform=matrix(.012,-0,0,-.012,43.226,16.2)><use xlink:href=#x39B/></g> </svg> and <svg style=vertical-align:-3.3907pt;width:52.787498px; id=M21 height=16.4 version=1.1 viewBox=0 0 52.787498 16.4 width=52.787498 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><use xlink:href=#x1D446/></g> <g transform=matrix(.012,-0,0,-.012,14.125,16.2)><use xlink:href=#x1D706/></g> <g transform=matrix(.017,-0,0,-.017,21.312,12.112)><use xlink:href=#x7D/></g> <g transform=matrix(.012,-0,0,-.012,27.213,16.2)><use xlink:href=#x1D706/></g><g transform=matrix(.012,-0,0,-.012,33.781,16.2)><use xlink:href=#x2208/></g><g transform=matrix(.012,-0,0,-.012,40.063,16.2)><use xlink:href=#x39B/></g> <g transform=matrix(.017,-0,0,-.017,48.85,12.112)><use xlink:href=#x2C/></g> </svg> respectively; <svg style=vertical-align:-3.3907pt;width:28.174999px; id=M22 height=16.4 version=1.1 viewBox=0 0 28.174999 16.4 width=28.174999 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><use xlink:href=#x1D6FC/></g> <g transform=matrix(.012,-0,0,-.012,15.613,16.2)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,22.213,12.112)><use xlink:href=#x7D/></g> </svg>, <svg style=vertical-align:-4.15506pt;width:28.4px; id=M23 height=17.4 version=1.1 viewBox=0 0 28.4 17.4 width=28.4 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.162)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.162)><use xlink:href=#x1D6FD/></g> <g transform=matrix(.012,-0,0,-.012,15.838,17.2)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,22.438,12.162)><use xlink:href=#x7D/></g> </svg>, <svg style=vertical-align:-4.15506pt;width:27.0375px; id=M24 height=17.35 version=1.1 viewBox=0 0 27.0375 17.35 width=27.0375 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><use xlink:href=#x1D6FE/></g> <g transform=matrix(.012,-0,0,-.012,14.475,17.15)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,21.075,12.112)><use xlink:href=#x7D/></g> </svg>, <svg style=vertical-align:-3.3907pt;width:28.174999px; id=M25 height=21.924999 version=1.1 viewBox=0 0 28.174999 21.924999 width=28.174999 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,17.65)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,17.65)><use xlink:href=#x1D6FC/></g> <g transform=matrix(.012,-0,0,-.012,15.613,9.488)><use xlink:href=#x2032/></g><g transform=matrix(.012,-0,0,-.012,15.613,21.725)><use xlink:href=#x1D45B/></g> <g transform=matrix(.017,-0,0,-.017,22.213,17.65)><use xlink:href=#x7D/></g> </svg>, <svg style=vertical-align:-4.15506pt;width:28.4px; 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Under some suitable conditions, a strong convergence theorem for common fixed points of the mappings <svg style=vertical-align:-3.3907pt;width:52.075001px; id=M33 height=16.4 version=1.1 viewBox=0 0 52.075001 16.4 width=52.075001 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><use xlink:href=#x1D447/></g> <g transform=matrix(.012,-0,0,-.012,17.287,16.2)><use xlink:href=#x1D706/></g> <g transform=matrix(.017,-0,0,-.017,24.475,12.112)><use xlink:href=#x7D/></g> <g transform=matrix(.012,-0,0,-.012,30.375,16.2)><use xlink:href=#x1D706/></g><g transform=matrix(.012,-0,0,-.012,36.943,16.2)><use xlink:href=#x2208/></g><g transform=matrix(.012,-0,0,-.012,43.226,16.2)><use xlink:href=#x39B/></g> </svg> and <svg style=vertical-align:-3.3907pt;width:48.912498px; id=M34 height=16.4 version=1.1 viewBox=0 0 48.912498 16.4 width=48.912498 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg> <g transform=matrix(.017,-0,0,-.017,.062,12.112)><use xlink:href=#x7B/></g><g transform=matrix(.017,-0,0,-.017,5.961,12.112)><use xlink:href=#x1D446/></g> <g transform=matrix(.012,-0,0,-.012,14.125,16.2)><use xlink:href=#x1D706/></g> <g transform=matrix(.017,-0,0,-.017,21.312,12.112)><use xlink:href=#x7D/></g> <g transform=matrix(.012,-0,0,-.012,27.213,16.2)><use xlink:href=#x1D706/></g><g transform=matrix(.012,-0,0,-.012,33.781,16.2)><use xlink:href=#x2208/></g><g transform=matrix(.012,-0,0,-.012,40.063,16.2)><use xlink:href=#x39B/></g> </svg> is obtained. The results extend those of the authors whose related researches are restricted to the situation of finite families of asymptotically nonexpansive mappings." @default.
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W2010618448 title "An Implicit Iteration Process for Common Fixed Points of Two Infinite Families of Asymptotically Nonexpansive Mappings in Banach Spaces" @default.
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