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• W2010400141 abstract "Let C be a closed, bounded and convex subset of a uniformly convex and uniformly smooth Banach space. Let {Tt}t≥0 be a strongly-continuous nonexpansive semigroup on C. Consider the iterative process defined by the sequence of equationsxk+1=ckTtk+1(xk+1)+(1−ck)xk. We prove that, under certain conditions, the sequence {xk} converges weakly to a common fixed point of the semigroup {Tt}t≥0. There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property. However, many important spaces like Lp for 1≤p≠2 do not possess the Opial property. In this paper, we do not assume the Opial property. We do assume instead that X is uniformly convex and uniformly smooth. Lp for p>1 are prime examples of such spaces." @default.
• W2010400141 created "2016-06-24" @default.
• W2010400141 creator A5000690711 @default.
• W2010400141 date "2015-06-01" @default.
• W2010400141 modified "2023-09-23" @default.
• W2010400141 title "On convergence of iteration processes for nonexpansive semigroups in uniformly convex and uniformly smooth Banach spaces" @default.
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• W2010400141 doi "https://doi.org/10.1016/j.jmaa.2015.02.021" @default.
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