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- W3120852804 abstract "In this paper, we prove a sufficient condition that every nonempty closed convex bounded pair <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mfenced open=( close=)> <mrow> <mi>M</mi> <mo>,</mo> <mi>N</mi> </mrow> </mfenced> </math> in a reflexive Banach space <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi>B</mi> </math> satisfying Opial’s condition has proximal normal structure. We analyze the relatively nonexpansive self-mapping <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <mi>T</mi> </math> on <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <mi>M</mi> <mo>∪</mo> <mi>N</mi> </math> satisfying <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi>T</mi> <mfenced open=( close=)> <mrow> <mi>M</mi> </mrow> </mfenced> <mo>⊆</mo> <mi>M</mi> </math> and <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <mi>T</mi> <mfenced open=( close=)> <mrow> <mi>N</mi> </mrow> </mfenced> <mo>⊆</mo> <mi>N</mi> </math> , to show that Ishikawa’s and Halpern’s iteration converges to the best proximity point. Also, we prove that under relatively isometry self-mapping <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <mi>T</mi> </math> on <math xmlns=http://www.w3.org/1998/Math/MathML id=M8> <mi>M</mi> <mo>∪</mo> <mi>N</mi> </math> satisfying <math xmlns=http://www.w3.org/1998/Math/MathML id=M9> <mi>T</mi> <mfenced open=( close=)> <mrow> <mi>N</mi> </mrow> </mfenced> <mo>⊆</mo> <mi>N</mi> </math> and <math xmlns=http://www.w3.org/1998/Math/MathML id=M10> <mi>T</mi> <mfenced open=( close=)> <mrow> <mi>M</mi> </mrow> </mfenced> <mo>⊆</mo> <mi>M</mi> </math> , Ishikawa’s iteration converges to the best proximity point in the collection of all Chebyshev centers of <math xmlns=http://www.w3.org/1998/Math/MathML id=M11> <mi>N</mi> </math> relative to <math xmlns=http://www.w3.org/1998/Math/MathML id=M12> <mi>M</mi> </math> . Some illustrative examples are provided to support our results." @default.
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- W3120852804 date "2021-01-07" @default.
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- W3120852804 title "Some Results on Iterative Proximal Convergence and Chebyshev Center" @default.
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- W3120852804 doi "https://doi.org/10.1155/2021/8863325" @default.
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