Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2022; 59(3): 595-619

Published online May 1, 2022 https://doi.org/10.4134/JKMS.j210443

Copyright © The Korean Mathematical Society.

Construction of a solution of split equality variational inequality problem for pseudomonotone mappings in Banach spaces

Getahun Bekele Wega

P.O. Box 378

Abstract

The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

Keywords: Monotone mapping, pseudomonotone mapping, split equality variational inequality problem, minimum point, zero points

MSC numbers: Primary 47J20, 47J05, 65K15, 47h09, 90C25

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