Convergence analysis of M-iteration for š¯’¢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems
Chonjaroen Chairatsiripong, Damrongsak Yambangwai, Tanakit Thianwan Ā· Demonstratio Mathematica Ā· 2023
Abstract In this article, weak and strong convergence theorems of the M-iteration method for š¯’¢-nonexpansive mapping in a uniformly convex Banach space with a directed graph were established. Moreover, weak convergence theorem without making use of Opialā€™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.