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...

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Veröffentlicht in:Demonstratio mathematica Jg. 58; H. 1; S. 133 - 181
Hauptverfasser: Yambangwai, Damrongsak, Thianwan, Tanakit
Format: Journal Article
Sprache:Englisch
Veröffentlicht: De Gruyter 29.01.2025
Schlagworte:
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
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Zusammenfassung: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