An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

Lateef Olakunle Jolaoso, Ferdinard Udochukwu Ogbuisi, Oluwatosin Temitope Mewomo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)

Abstract

In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

Original languageEnglish
Pages (from-to)167-184
Number of pages18
JournalAdvances in Pure and Applied Mathematics
Volume9
Issue number3
DOIs
Publication statusPublished - 1 Jul 2018
Externally publishedYes

Keywords

  • Bregman distance
  • Bregman projection
  • Fréchet differentiable functions
  • Gâteaux differentiable function
  • Legendre functions
  • convex minimization problem
  • reffexive Banach space
  • resolvent
  • strong convergence
  • variational inequality

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