Fixed point results for a pair of mappings in Banach space for enriched contraction condition with application in integral calculus

The purpose of this paper is to establish some new common fixed point results for a pair of conditionally sequential absorbing self-mappings satisfying an enriched contraction condition in Banach space by introducing the notion of weaker form of continuity. We have also illustrated an example in support of our main result. Further, to make our result more effective, we have established the existence and the uniqueness of the solution of an Integral equation as an application of our main result with an example.