FIXED POINT RESULTS FOR INTERPOLATIVE HARDY-ROGERS-MEIR-KEELER CONTRACTIONS WITH APPLICATION

Abstract

In this paper, we introduce a new class of contractions in metric spaces, calledinterpolative Hardy-Rogers-Meir-Keeler-type contractions. This class generalizes and unifies several well-known fixed point principles by incorporating interpolative techniques and Meir-Keeler-type conditions into the Hardy-Rogers framework. We establish a fixed point theoremfor such mappings in complete metric spaces, ensuring the existence and uniqueness of fixed points. To demonstrate the applicability of our results, we apply the developed theorem toprove the existence and uniqueness of solutions to a class of nonlinear Hammerstein integralequations. An illustrative example is provided to support the main results.