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.
Highlights
In the literature of metric fixed point theory, the Banach contraction principle is well known
We develop a new parallel algorithm based on the Ishikawa iteration process with the inertial technique to prove the weak convergence theorem for estimating common fixed points of a finite family of G-nonexpansive mappings by assuming some control conditions in Hilbert spaces endowed with a directed graph
5 Conclusion In summary, we present a new parallel algorithm that solves the common fixed point problem for a finite family of G-nonexpansive mappings by combining the Ishikawa iteration process with the inertial technique
Summary
In the literature of metric fixed point theory, the Banach contraction principle is well known. We develop a new parallel algorithm based on the Ishikawa iteration process with the inertial technique to prove the weak convergence theorem for estimating common fixed points of a finite family of G-nonexpansive mappings by assuming some control conditions in Hilbert spaces endowed with a directed graph.
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