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
Damrongsak Yambangwai, Tanakit Thianwan · Demonstratio Mathematica · 2025
Abstract 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 R 2 ${\mathbb{R}}^{2}$ 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.