Results in Fixed Point Theorems for Relational-Theoretic Contraction Mappings in Metric Spaces

Abstract

The purpose of this article is to extend the classical Banach contraction principle to a complete metric space endowed with a binary relation where the contraction condition is relatively weaker than usual contraction as it is required to hold only on those elements which are related under the underlying relation rather than the whole space. Finally, we apply our results to prove the existence and uniqueness of solution of a certain class of nonlinear contraction in a complete metric space. The presented theorems extend and subsumes various known comparable results from the current literature. Some illustrative examples and applications are provided to demonstrate the main results and to show the genuineness of our results.