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Composite implicit random iterations for approximating common random fixed point for a finite family of asymptotically nonexpansive random operators

Shrabani Banerjee|Binayak S. Choudhury
대한수학회 (The Korean Mathematical Society)|2011.01|대한수학회논문집 (Communications of the KMS)|제26권 제1호|pp. 23-35

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참고문헌

키워드

Banach spacesasymptotically nonexpansive random operatorsCondition(B)measurable spaces
주제분류수학

초록

In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

Abstract

In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

참고문헌 (21)

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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 theorems of a finite family of asymptotically quasi-nonexpansive type mappings in Banach spacesGurucharan Singh Saluja영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호Convergence of an Implicit Iterative Process for Two Finite Families of Nonexpansive Mappings강신민, 권영철, 조선영, Xiaolong Qin강원경기수학회 · 한국수학논문집2010 · 제18권 제3호STRONG CONVERGENCE OF COMPOSITE IMPLICIT ITERATIVE PROCESS FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGSFeng Gu영남수학회 · East Asian Mathematical Journal2008 · 제24권 제1호Some strong convergence results of random iterative algorithms with errors in Banach spacesRenu Chugh, Satish Narwal, Vivek Kumar대한수학회 · 대한수학회논문집2016 · 제31권 제1호CONVERGENCE THEOREMS OF IMPLICIT ITERATION PROCESS WITH ERRORS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE IN BANACH SPACESG. S. Saluja영남수학회 · East Asian Mathematical Journal2012 · 제28권 제1호

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