Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications

Journal article

Authors/Editors

Strategic Research Themes

Publication Details

Author list: Adamu, Abubakar; Kumam, Poom; Kitkuan, Duangkamon; Padcharoen, Anantachai;

Publication year: 2023

Journal: Carpathian Journal of Mathematics (1843-4401)

Volume number: 39

Issue number: 1

Start page: 1

End page: 26

Number of pages: 26

ISSN: 1843-4401

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85144163368&doi=10.37193%2fCJM.2023.01.01&partnerID=40&md5=27a578f4136e784c9cc66629368b5085

Languages: English-Great Britain (EN-GB)

View in Web of Science | View on publisher site | View citing articles in Web of Science

Abstract

In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature. © 2023, SINUS Association. All rights reserved.

Keywords

J-fixed point, relaxed, Tseng algorithm, zeros