Common fixed point under Jungck contractive condition in a digital metric space

Abstract

Digital topology is concerned with the topological characteristics of digital image pictures or objects. A peculiar arrangement of non-negative numbers configures digital images. Digital image processing is a technique of dismantling the picture into its fundamental components and analyzing its various features with respect to component parts. In analyzing the fundamental segments of image pictures, the connected segments are separated out to ascertain the relationship of adjacency. During this process of tracking, coding and thinning, it is kept in mind that the connectedness peculiarity of the object remains unchanged.

The features of the component subsets and their relationships can be detailed when the image is decomposed into its constituents. Some of the characteristics of these constituent points or subsets are depending on their positions. Thus, the primary topological features of digital images like connectedness, adjacency, etc. can be the basic clues for their processing.

Various kinds of contraction mappings and related fixed-point theorems can be applied in the field of science and technology, including mathematics, game theory, computer science, engineering, environmental science, etc. Fix point theorems are applied in computational techniques in engineering and science to explore the areas of parallel and distributed computation, simulation, modeling and image processing-digital images. In image processing fixed point theorems are applied to get digital contraction which would be a mathematical basis of contour filling, border following algorithm and thinning of a digital image.

To broaden the applicability of contraction principle and associated fixed point theorem in image processing, we wish to explore some of them as significant applicable tools for digital image processing.