Modified Tseng Method for Solving Pseudomonotone Variational Inequality Problem in Banach Spaces

Rose Maluleka, Godwin Chidi Ugwunnadi*, Maggie Aphane, Hammed A. Abass, Abdul Rahim Khan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This article examines the process for solving the fixed-point problem of Bregman strongly nonexpansive mapping as well as the variational inequality problem of the pseudomonotone operator. Within the context of p-uniformly convex real Banach spaces that are also uniformly smooth, we introduce a modified Halpern iterative technique combined with an inertial approach and Tseng methods for finding a common solution of the fixed-point problem of Bregman strongly nonexpansive mapping and the pseudomonotone variational inequality problem. Using our iterative approach, we develop a strong convergence result for approximating the solution of the aforementioned problems. We also discuss some consequences of our major finding. The results presented in this paper complement and build upon many relevant discoveries in the literature.

Original languageEnglish
Article number363
JournalSymmetry
Volume16
Issue number3
DOIs
Publication statusPublished - Mar 2024

Keywords

  • Banach space
  • Bregman strongly nonexpansive mapping
  • fixed point
  • strongly nonexpansive mapping
  • variational inequality problem

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