A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces

Lateef Olakunle Jolaoso*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a self-adaptive projection method for finding a common element in the solution set of variational inequalities (VIs) and fixed point set for relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth real Banach spaces. We prove a strong convergence result for the sequence generated by our algorithm without imposing a Lipschitz condition on the cost operator of the VIs. We also provide some numerical examples to illustrate the performance of the proposed algorithm by comparing with related methods in the literature. This result extends and improves some recent results in the literature in this direction.

Original languageEnglish
Pages (from-to)527-547
Number of pages21
JournalDemonstratio Mathematica
Volume54
Issue number1
DOIs
Publication statusPublished - 1 Jan 2021

Keywords

  • Banach spaces
  • monotone operator
  • projection method
  • self-adaptive
  • variational inequality

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