A parallel monotone hybrid algorithm for a finite family of G- nonexpansive mappings in Hilbert spaces endowed with a graph applicable in signal recovery

Abstract

In this paper, we modified the shrinking projection method with the parallel monotone hybrid method for approximating common fixed points of a finite family of G-nonexpansive mappings. We then prove a strong convergence theorem under suitable conditions in Hilbert spaces endowed with graphs. Moreover, we give some numerical examples and compare the rate of convergence of our algorithms. Finally, we provide an application to signal recovery in a situation without knowing the type of noises and demonstrate the computational performance of our algorithm in comparison to some methods. The numerical results of the comparative analysis are also discussed.