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HALPERN ITERATION PROCESS FOR APPROXIMATING SOLUTIONS OF MONOTONE YOSIDA VARIATIONAL INCLUSION, MINIMIZATION AND FIXED POINT PROBLEMS

HAMMED ANUOLUWAPO ABASS|AKINDELE ADEBAYO MEBAWONDU
장전수학회 (Jangjeon Mathematical Society)|2022.01|Advanced Studies in Contemporary Mathematics|제32권 제1호|pp. 17-30

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참고문헌

키워드

Fixed point problemminimization problemsemigroup nonexpansive mappinginertial iterative scheme
주제분류수학

초록

In this paper, we introduce an Halpern type iterative algorithm to approxi- mate a common solution of monotone yosida variational inclusion problem, minimization problem and fixed point problem of finite family of quasi pseudo-contractive mappings in the framework of real Hilbert space. Using our iterative algorithm, we prove a strong convergence theorem of the aforementioned problems without imposing the compactness condition on our mapping. W also give an application of our main result to variational inequality problem. The result discuss in this paper extends and complements some related results in literature.

Abstract

In this paper, we introduce an Halpern type iterative algorithm to approxi- mate a common solution of monotone yosida variational inclusion problem, minimization problem and fixed point problem of finite family of quasi pseudo-contractive mappings in the framework of real Hilbert space. Using our iterative algorithm, we prove a strong convergence theorem of the aforementioned problems without imposing the compactness condition on our mapping. W also give an application of our main result to variational inequality problem. The result discuss in this paper extends and complements some related results in literature.

참고문헌 (33)

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관련 논문AI추천

WEAK CONVERGENCE THEOREMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, MONOTONE MAPPINGS AND PSEUDOCONTRACTIVE MAPPINGS정종수대한수학회 · 대한수학회지2015 · 제52권 제6호General iterative algorithms for monotone inclusion, variational inequality and fixed point problems정종수대한수학회 · 대한수학회지2021 · 제58권 제3호APPROXIMATION OF SOLUTIONS OF A GENERALIZED VARIATIONAL INEQUALITY PROBLEM BASED ON ITERATIVE METHODS조선영대한수학회 · 대한수학회논문집2010 · 제25권 제2호Solutions of systems of variational inequalities on fixed points of nonexpansive mappingsHossein Piri대한수학회 · 대한수학회보2014 · 제51권 제3호GENERAL NONLINEAR VARIATIONAL INCLUSIONS WITH H-MONOTONE OPERATOR IN HILBERT SPACES강신민, Pingping Zheng, Tao Cai, Zeqing Liu대한수학회 · 대한수학회보2010 · 제47권 제2호An iteration schemes for nonexpansive mappings and variational inequalitiesHongjun Wang, Yisheng Song대한수학회 · 대한수학회보2011 · 제48권 제5호

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