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Strong convergence of an iterative method for finding common zeros of a finite family of accretive operators

정종수
대한수학회 (The Korean Mathematical Society)|2009.07|대한수학회논문집 (Communications of the KMS)|제24권 제3호|pp. 381-393

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참고문헌

키워드

resolventfixed pointsstrong convergencenonexpansive mappingstrictly convexsunny and nonexpansive retractionaccretive operatorvariational inequalitiesuniformly Gateaux differentiable norm
주제분류수학

초록

Strong convergence theorems on viscosity approximation me\-thods for finding a common zero of a finite family accretive operators are established in a reflexive and strictly Banach space having a uniformly Gateaux differentiable norm. The main theorems supplement the recent corresponding results of Wong et al. [29] and Zegeye and Shahzad [32] to the viscosity method together with different control conditions. Our results also improve the corresponding results of [9,16,18,19,25] for finite nonexpansive mappings to the case of finite pseudocontractive mappings.

Abstract

Strong convergence theorems on viscosity approximation me\-thods for finding a common zero of a finite family accretive operators are established in a reflexive and strictly Banach space having a uniformly Gateaux differentiable norm. The main theorems supplement the recent corresponding results of Wong et al. [29] and Zegeye and Shahzad [32] to the viscosity method together with different control conditions. Our results also improve the corresponding results of [9,16,18,19,25] for finite nonexpansive mappings to the case of finite pseudocontractive mappings.

참고문헌 (32)

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관련 논문AI추천

New iterative algorithms for zeros of accretive operatorsYisheng Song대한수학회 · 대한수학회지2009 · 제46권 제1호Viscosity methods of approximation for a common solution of a finite family of accretive operatorsJun-Min Chen, Li-Juan Zhang, Tie-Gang Fan영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호Strong Convergence Theorems for Common Points of a Finite Family of Accretive Operators김수환, 정재욱경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제3호CONVERGENCE THEOREMS ON VISCOSITY APPROXIMATION METHODS FOR FINITE NONEXPANSIVE MAPPINGS IN BANACH SPACES정종수한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제1호Strong convergence of an iterative algorithm for a modified system of variational inequalities and a finite family of nonexpansive mappings in Banach spaces정재욱강원경기수학회 · 한국수학논문집2015 · 제23권 제3호STRONG CONVERGENCE OF AN IMPLICIT ITERATIVE PROCESS FOR AN INFINITE FAMILY OF STRICT PSEUDOCONTRACTIONS강신민, 조열제, Xiaolong Qin대한수학회 · 대한수학회보2010 · 제47권 제6호

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