INERTIAL PROXIMAL AND CONTRACTION METHODS FOR SOLVING MONOTONE VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS

Jacob Ashiwere Abuchu*, Godwin Chidi Ugwunnadi, Ojen Kumar Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

Original languageEnglish
Pages (from-to)175-203
Number of pages29
JournalNonlinear Functional Analysis and Applications
Volume28
Issue number1
DOIs
Publication statusPublished - 2023
Externally publishedYes

Keywords

  • Monotone variational inclusion problem
  • inertial iterative method
  • nonexpansive operator
  • pseudocontractive operator
  • resolvent operator
  • strong convergence

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