A strong convergence halpern-type inertial algorithm for solving system of split variational inequalities and fixed point problems

A. A. Mebawondu, L. O. Jolaoso*, H. A. Abass, O. K. Oyewole, K. O. Aremu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we propose a new Halpern-type inertial extrapola-tion method for approximating common solutions of the system of split varia-tional inequalities for two inverse-strongly monotone operators, the variational inequality problem for monotone operator, and the fixed point of composi-tion of two nonlinear mappings in real Hilbert spaces. We establish that the proposed method converges strongly to an element in the solution set of the aforementioned problems under certain mild conditions. In addition, we present some numerical experiments to show the efficiency and applicability of our method in comparison with some related methods in the literature. This result improves and generalizes many recent results in this direction in the literature.

Original languageEnglish
Pages (from-to)2762-2791
Number of pages30
JournalJournal of Applied Analysis and Computation
Volume11
Issue number6
DOIs
Publication statusPublished - 2021

Keywords

  • Firmly nonexpansive
  • Fixed point problem
  • Generalized system of variational inequality problem
  • Inertial iterative scheme
  • Split feasibility problem

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