Inertial Extragradient Method for Solving Variational Inequality and Fixed Point Problems of a Bregman Demigeneralized Mapping in a Reflexive Banach Spaces

H. A. Abass, G. C. Godwin, O. K. Narain, V. Darvish*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, by employing a Bregman distance approach, we introduce a self-adaptive inertial extragradient method for finding a common solution of variational inequality problem involving a pseudo-monotone operator and fixed point problem of a Bregman demigeneralized mapping in a reflexive Banach spaces. Using a Bregman distance approach, we establish a strong convergence result for approximating the common solution of the aforementioned problems under some mild assumptions. We display some numerical examples to show the performance of our iterative method. The result presented in this paper extends and complements many related results in literature.

Original languageEnglish
Pages (from-to)933-960
Number of pages28
JournalNumerical Functional Analysis and Optimization
Volume43
Issue number8
DOIs
Publication statusPublished - 2022
Externally publishedYes

Keywords

  • Bregman demigeneralized mapping
  • fixed point problem
  • iterative scheme
  • pseudo-monotone operator
  • variational inequality problem

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