Convergence analysis of M-iteration for \(\mathcal{G}\)-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems. (English) Zbl 07720273
Summary: In this article, weak and strong convergence theorems of the M-iteration method for \(\mathcal{G}\)-nonexpansive mapping in a uniformly convex Banach space with a directed graph are established. Moreover, a weak convergence theorem is proved without making use of Opial’s condition. The rate of convergence between the M-iteration and some other iteration processes in the literature is 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 are given. As application, some numerical experiments in real-world problems are provided, focused on image deblurring and signal recovering problems.
MSC:
| 47J26 | Fixed-point iterations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 47N70 | Applications of operator theory in systems, signals, circuits, and control theory |
Keywords:
\(\mathcal{G}\)-nonexpansive mapping; M-iteration method; signal recovery problem; image deblurring problem; strong convergence; uniformly convex Banach space with a directed graph; weak convergence; three-step Noor iteration; SP-iterationReferences:
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