A Totally Relaxed, Self-Adaptive Subgradient Extragradient Method for Variational Inequality and Fixed Point Problems in a Banach Space

Lateef Olakunle Jolaoso, Adeolu Taiwo, Timilehin Opeyemi Alakoya, Oluwatosin Temitope Mewomo*, Qiao Li Dong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a Totally Relaxed Self-adaptive Subgradient Extragradient Method (TRSSEM) with Halpern iterative scheme for finding a common solution of a Variational Inequality Problem (VIP) and the fixed point of quasi-nonexpansive mapping in a 2-uniformly convex and uniformly smooth Banach space. The TRSSEM does not require the computation of projection onto the feasible set of the VIP; instead, it uses a projection onto a finite intersection of sub-level sets of convex functions. The advantage of this is that any general convex feasible set can be involved in the VIP. We also introduce a modified TRSSEM which involves the projection onto the set of a convex combination of some convex functions. Under some mild conditions, we prove a strong convergence theorem for our algorithm and also present an application of our theorem to the approximation of a solution of nonlinear integral equations of Hammerstein's type. Some numerical examples are presented to illustrate the performance of our method as well as comparing it with some related methods in the literature. Our algorithm is simple and easy to implement for computation.

Original languageEnglish
Pages (from-to)73-95
Number of pages23
JournalComputational Methods in Applied Mathematics
Volume22
Issue number1
DOIs
Publication statusPublished - 1 Jan 2022
Externally publishedYes

Keywords

  • Extragradient Method
  • Hammerstein Equation
  • Nonexpansive Mappings
  • Subgradient Method
  • Total Relaxed
  • Variational Inequality

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