An inertial parallel algorithm for a finite family of G-nonexpansive mappings with application to the diffusion problem
Phakdi Charoensawan, Damrongsak Yambangwai, Watcharaporn Cholamjiak, Raweerote Suparatulatorn · Advances in Difference Equations · 2021
Abstract For finding a common fixed point of a finite family of G-nonexpansive mappings, we implement a new parallel algorithm based on the Ishikawa iteration process with the inertial technique. We obtain the weak convergence theorem of this algorithm in Hilbert spaces endowed with a directed graph by assuming certain control conditions. Furthermore, numerical experiments on the diffusion problem demonstrate that the proposed approach outperforms well-known approaches.