Convergence of Picard–CR Iterative Algorithm and Applications
Journal of Function Spaces, vol.2026, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2026 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1155/jofs/3625869
- Journal Name: Journal of Function Spaces
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
- Keywords: digraph, fixed point, image deblurring, signal enhancement
- Ataturk University Affiliated: Yes
Abstract
In applied mathematics, graph theory (GT) is a notably compelling area of study. In the last 50 years, the number of mathematicians making contributions to research in this field has consistently increased. This rising interest is mainly a result of the significant real-world applications it offers. It has been utilized in various areas of study such as engineering, physical sciences, genetics, computer science, sociology, operations research, and economics. Grounded in these foundational ideas, we introduce and conduct an in-depth analysis of the convergence theorems for the Picard–CR iterative sequences applied to G-nonexpansive mapping in Banach spaces via a graph. In addition, Picard–CR iterative algorithm′s applications to image deblurring and refining (or denoising) a signal are illustrated.