SOLVING SYSTEM OF SPLIT COMMON FIXED POINT AND MONOTONE VARIATIONAL INCLUSION PROBLEMS VIA DYNAMICAL STEP-SIZE IN BANACH SPACES

H. A. Abass, G. C. Ugwunnadi, O. K. Narain*, A. R. Khan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we investigate a self adaptive accelerated method for solving split common fixed point problem for a finite family of firmly-nonexpansive type mappings (Type P) and monotone variational inclusion problem in p-uniformly convex and uniformly smooth Banach spaces. Using a modified Halpern method together with an inertial extrapolation method, we prove a strong convergence theorem for solving the aforementioned problems. The implementation of our iterative method does not require prior knowledge of the operator norm. We also provide some numerical examples to show better performance of our method. Our results extend and complement many related results existing in the literature.

Original languageEnglish
Pages (from-to)1149-1172
Number of pages24
JournalNonlinear Functional Analysis and Applications
Volume29
Issue number4
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • Monotone variational inclusion problem
  • firmly nonexpansive-type mapping
  • fixed point problem
  • inertial method
  • split feasibility problem

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