Convergence analysis for variational inequalities and fixed point problems in reflexive Banach spaces

Lateef Olakunle Jolaoso, Yekini Shehu*, Yeol Je Cho

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, using a Bregman distance technique, we introduce a new single projection process for approximating a common element in the set of solutions of variational inequalities involving a pseudo-monotone operator and the set of common fixed points of a finite family of Bregman quasi-nonexpansive mappings in a real reflexive Banach space. The stepsize of our algorithm is determined by a self-adaptive method, and we prove a strong convergence result under certain mild conditions. We further give some applications of our result to a generalized Nash equilibrium problem and bandwidth allocation problems. We also provide some numerical experiments to illustrate the performance of our proposed algorithm using various convex functions and compare this algorithm with other algorithms in the literature.

Original languageEnglish
Article number44
JournalJournal of Inequalities and Applications
Volume2021
Issue number1
DOIs
Publication statusPublished - 2021

Keywords

  • Banach spaces
  • Bregman distance
  • Fixed point
  • Projection method
  • Variational inequality

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