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An iteration schemes for nonexpansive mappings and variational inequalities

Yisheng Song|Hongjun Wang
대한수학회 (The Korean Mathematical Society)|2011.09|대한수학회보 (Bulletin of the KMS)|제48권 제5호|pp. 991-1002

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참고문헌

키워드

strong convergencevariational inequalitynonexpansive mappinginverse-strongly monotone mappingmetric projection
주제분류수학

초록

An iterative algorithm is provided to find a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of some variational inequality in a Hilbert space. Using this result, we consider a strong convergence result for finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping. Our results include the previous results as special cases and can be viewed as an improvement and refinement of the previously known results.

Abstract

An iterative algorithm is provided to find a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of some variational inequality in a Hilbert space. Using this result, we consider a strong convergence result for finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping. Our results include the previous results as special cases and can be viewed as an improvement and refinement of the previously known results.

참고문헌 (31)

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관련 논문AI추천

Strong convergence theorems for asymptotically quasi-nonexpansive mappings and inverse-strongly monotone mappingsXin-feng He, Yong-chun Xu, Zhen He영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호Solutions of systems of variational inequalities on fixed points of nonexpansive mappingsHossein Piri대한수학회 · 대한수학회보2014 · 제51권 제3호STRONG CONVERGENCE OF EXTENDED GENERAL VARIATIONAL INEQUALITIES AND NONEXPANSIVE MAPPINGSJun-Min Chen, Li-Juan Zhang, Zhen He영남수학회 · East Asian Mathematical Journal2010 · 제26권 제1호General iterative algorithms for monotone inclusion, variational inequality and fixed point problems정종수대한수학회 · 대한수학회지2021 · 제58권 제3호STRONG CONVERGENCE THEOREMS FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY-MONOTONE MAPPINGS IN A BANACH SPACEYing Liu영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호Strong convergence of an iterative algorithm for a modified system of variational inequalities and a finite family of nonexpansive mappings in Banach spaces정재욱강원경기수학회 · 한국수학논문집2015 · 제23권 제3호

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