Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces

Abstract

In this paper, we proved some coincidence point results for $f$-nondecreasing self-mapping satisfying certain rational type contractions in the context of a metric space endowed with a partial order. Moreover, some consequences of the main result are given by involving integral type contractions in the space. Some numerical examples are illustrated to support our results. As an application, we have discussed the existence of a unique solution of integral equation.

Keywords

• ordered metric spaces
• rational contractions
• compatible mappings
• weakly compatible mappings
• coupled fixed point
• common fixed point