Solving Periodic Boundary Value Problem via Product Type Rational Contractions

Abstract

In this paper, we define some new product types of rational contractions for single-valued mappings in generalized metric spaces. We prove the uniqueness of fixed point (FP) and common fixed point (CFP) theorems under the new product types of rational contractions in generalized metric spaces with the application of boundary value problem. In support of our results, we present nontrivial illustrative examples for the uniqueness of FP and CFP in generalized metric spaces. Furthermore, we present an application of the first-order periodic boundary value problem for the existence of unique solutions to unify our work. Using this approach, one can prove some more attractive unique FP and CFP results for different types of modified rational contractions in generalized metric spaces with the application of integral equations and boundary value problems.