Convergence results of forward–backward method for a zero of the sum of maximally monotone mappings in Banach spaces

Getahun Bekele Wega, Habtu Zegeye

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1 Citation (Scopus)

Abstract

The purpose of this paper is to study a forward–backward algorithm for approximating a zero of the sum of maximally monotone mappings in the setting of Banach spaces. Under some mild conditions, we prove a new strong convergence theorem for the algorithm produced by the method in real reflexive Banach spaces. In addition, we give some applications to the minimization problems. Finally, we provide a numerical example, which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Original languageEnglish
Article number223
Number of pages16
JournalComputational and Applied Mathematics
Volume39
Issue number3
DOIs
Publication statusPublished - Sep 1 2020

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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