Inertial Method for Solving Pseudomonotone Variational Inequality and Fixed Point Problems in Banach Spaces

Author:

Maluleka Rose12,Ugwunnadi Godwin Chidi13ORCID,Aphane Maggie1ORCID

Affiliation:

1. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Pretoria 0204, South Africa

2. Department of Mathematics and Statistics, Tshwane University of Technology, Staatsartillerie Rd, Pretoria West, Pretoria 0183, South Africa

3. Department of Mathematics, Faculty of Science and Engineering, University of Eswatini, Private Bag 4, Kwaluseni M201, Eswatini

Abstract

In this paper, we introduce a new iterative method that combines the inertial subgradient extragradient method and the modified Mann method for solving the pseudomonotone variational inequality problem and the fixed point of quasi-Bregman nonexpansive mapping in p-uniformly convex and uniformly smooth real Banach spaces. Under some standard assumptions imposed on cost operators, we prove a strong convergence theorem for our proposed method. Finally, we perform numerical experiments to validate the efficiency of our proposed method.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference42 articles.

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