ALTERNATED INERTIAL RELAXED TSENG METHOD FOR SOLVING FIXED POINT AND QUASI-MONOTONE VARIATIONAL INEQUALITY PROBLEMS

A. E. Ofem*, A. A. Mebawondu, C. Agbonkhese, G. C. Ugwunnadi, O. K. Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ -demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

Original languageEnglish
Pages (from-to)131-164
Number of pages34
JournalNonlinear Functional Analysis and Applications
Volume29
Issue number1
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • fixed point
  • quasimonotone operator
  • strong convergence and linear convergence
  • Tseng method
  • Variational inequality problem

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