Investigating the modified UO-iteration process in Banach spaces by a digraph

Abstract Graph theory (GT) is a highly captivating area of study within applied mathematics. Over the last 50 years, the number of mathematicians contributing to research in this field has consistently risen. This surge in interest can largely be attributed to its vast potential for practical applications. It has found uses in various disciplines such as engineering, physical sciences, genetics, computer science, sociology, operations research and economics. Driven and encouraged by these points, we introduce and analyze the convergence theorems for the modified UO-iterative sequences applied to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>G</m:mi> </m:math> G -nonexpansive mapping in Banach spaces via a graph. In addition, the modified UO-iterative algorithm’s applications to image deblurring and signal enhancement are demonstrated.