A parallel inertial three-step iteration monotone hybrid algorithm for a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs applicable to signal recovery problems

In this paper, we present a new computational approach named the parallel inertial three-step iteration monotone hybrid algorithm (abbreviated as PITMHA), devised for addressing the common fixed point problem of a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs. We est...

Full description

Saved in:

Bibliographic Details
Published in:	Demonstratio mathematica Vol. 58; no. 1; pp. 133 - 181
Main Authors:	Yambangwai, Damrongsak, Thianwan, Tanakit
Format:	Journal Article
Language:	English
Published:	De Gruyter 29.01.2025
Subjects:	47E10 47H09 47H10 54H25 common fixed point G-nonexpansive mapping parallel inertial three-step iteration signal recovery problem weak convergence
ISSN:	2391-4661, 2391-4661
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	In this paper, we present a new computational approach named the parallel inertial three-step iteration monotone hybrid algorithm (abbreviated as PITMHA), devised for addressing the common fixed point problem of a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs. We establish a theorem demonstrating weak convergence for PITMHA. To emphasize our results, we offer an example of G-nonexpansive mappings on endowed with a graph. This brings to light a new method that allows the visualization of some convergence behaviours. Furthermore, we demonstrate the practical utility of PITMHA by applying it to solve signal recovery problems.
ISSN:	2391-4661 2391-4661
DOI:	10.1515/dema-2025-0184