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Convergence theorems of a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces

Gurucharan Singh Saluja
영남수학회 (Youngnam Mathematical Society)|2011.01|East Asian Mathematical Journal|제27권 제1호|pp. 35-49

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참고문헌

키워드

strong convergenceuniformly convex Banach spacecommon fixed pointAsymptotically quasi-nonexpansive type mappingmulti-step iterative algorithm with errorsuniformly (Lα)-Lipschitz mapping
주제분류수학

초록

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to common fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family of said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

Abstract

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to common fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family of said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

참고문헌 (20)

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관련 논문AI추천

CONVERGENCE TO COMMON FIXED POINTS FOR A FINITE FAMILY OF GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACESG. S. Saluja영남수학회 · East Asian Mathematical Journal2013 · 제29권 제1호Convergence of modified multi-step iterative for a finite family of asymptotically quasi-nonexpansive mappingsJuan Xiao, Lei Deng, Ming-ge Yang대한수학회 · 대한수학회논문집2014 · 제29권 제1호CONVERGENCE THEOREMS OF MULTI-STEP ITERATIVE SCHEMES WITH ERRORS FOR ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE NONSELF MAPPINGS김종규, G. S. Saluja, Hemant Kumar Nashine영남수학회 · East Asian Mathematical Journal2010 · 제26권 제1호Convergence of an Implicit Iterative Process for Two Finite Families of Nonexpansive Mappings강신민, 권영철, 조선영, Xiaolong Qin강원경기수학회 · 한국수학논문집2010 · 제18권 제3호On iterative approximation of common fixed points of asymptotically nonexpansive mappings with applications김종규, 임원희, Xiaolong Qin영남수학회 · East Asian Mathematical Journal2012 · 제28권 제5호Weak and strong convergence of three step iteration scheme with errors for non-self asymptotically nonexpansive mappings권영철, 정재욱강원경기수학회 · 한국수학논문집2014 · 제22권 제2호

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