EXPLORING COMMUTATIVE FUNCTIONS IN DIGITAL METRIC SPACES FOR CONTRACTION-TYPE FIXED POINT IN DIGITAL IMAGE PROCESSING

Abstract

Considering the important role of fixed point theorem in both pure and applied mathematics, many researchers over the years have extensively presented different fixed point results for various contraction type mapping and their applications. This research proposes commutative functions in digital metric spaces for contraction type fixed point theorem in digital image processing and explores the application of contraction and commutative techniques in digital metric spaces to obtained the existence and uniqueness of a fixed point. We suggested two commuting functions for Zamfirescu contraction type mapping and Hardy-Rogers contraction type fixed point theorem for digital image and metric spaces. The results demonstrated the effectiveness of image processing techniques in enhancing digital image quality. The outcomes meet the Banach contraction principle's existence and uniqueness requirements for a digital contraction mapping in digital metric space.