A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications

Abstract

In this work, we aim to prove the strong convergence of the sequence generated by the modified inertial parallel viscosity-type algorithm for finding a common fixed point of a finite family of nonexpansive mappings under mild conditions in real Hilbert spaces. Moreover, we present the numerical experiments to solve linear systems and differential problems using Gauss–Seidel, weight Jacobi, and successive over relaxation methods. Furthermore, we provide our algorithm to show the efficiency and implementation of the LASSO problems in signal recovery. The novelty of our algorithm is that we show that the algorithm is efficient compared with the existing algorithms.

Keywords

• strong convergence
• parallel algorithm
• nonexpansive mappings
• inertial technique