Convergence of Picard–CR Iterative Algorithm and Applications

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.