Convergence analysis of M-iteration for 𝒢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems

Abstract

In this article, weak and strong convergence theorems of the M-iteration method for 𝒢-nonexpansive mapping in a uniformly convex Banach space with a directed graph were established. Moreover, weak convergence theorem without making use of Opial’s condition is proved. The rate of convergence between the M-iteration and some other iteration processes in the literature was also compared. Specifically, our main result shows that the M-iteration converges faster than the Noor and SP iterations. Finally, the numerical examples to compare convergence behavior of the M-iteration with the three-step Noor iteration and the SP-iteration were given. As application, some numerical experiments in real-world problems were provided, focused on image deblurring and signal recovering problems.

Keywords

• g-nonexpansive mapping
• m-iteration method
• signal recovering problem
• image deblurring problem
• directed graph
• 46t99
• 47h09
• 47h10
• 47j25
• 49m37
• 54h25