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Approximating fixed points of nonexpansive type mappings in Banach spaces without uniform convexity

강신민|Abdul Rahim Khan|Daya Ram Sahu
대한수학회 (The Korean Mathematical Society)|2013.05|대한수학회보 (Bulletin of the KMS)|제50권 제3호|pp. 1007-1020

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참고문헌

키워드

Mann iterationasymptotically nonexpansive mappingnearly asymptotically nonexpansive mappingnearly uniform k-contraction mappingOpial condition.
주제분류수학

초록

Approximate fixed point property problem for Mann itera- tion sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65–71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpan- sive mappings on an arbitrary normed space. Our results generalize and extend several known results.

Abstract

Approximate fixed point property problem for Mann itera- tion sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65–71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpan- sive mappings on an arbitrary normed space. Our results generalize and extend several known results.

참고문헌 (30)

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관련 논문AI추천

On iterative approximation of common fixed points of asymptotically nonexpansive mappings with applications김종규, 임원희, Xiaolong Qin영남수학회 · East Asian Mathematical Journal2012 · 제28권 제5호Strong convergence of modified ishikawa iterates for asymptotically nonexpansive maps with new control conditionsA. Anthony Eldred, P. Julia Mary대한수학회 · 대한수학회논문집2018 · 제33권 제4호Approximation of Common Fixed Points of Mean Non-expansive Mapping in Banach SpacesGu Zhaohui, Li Yongjin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호Strong convergence of modified Ishikawa iteration for two relatively nonexpansive mappings in a Banach spaceXian Wang, Ying Liu, Zhen He영남수학회 · East Asian Mathematical Journal2009 · 제25권 제1호Convergence theorems of a finite family of asymptotically quasi-nonexpansive type mappings in Banach spacesGurucharan Singh Saluja영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호Convergence theorems of the modified Ishikawa iterative process for nonexpansive mappings강신민, 이석진영남수학회 · East Asian Mathematical Journal2009 · 제25권 제1호

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