Fixed Point Results for Generalized Hardy-Rogers Type Interpolative Contraction in Partial and Partial b-Metric Spaces

Abstract

In this paper, we revisit fixed point results in partial metric spaces and introduce the notion of a generalized Hardy--Rogers type interpolative contraction within the framework of complete partial metric spaces and complete partial b-metric spaces. By combining the linear structure of Hardy--Rogers contractions with nonlinear power-type interpolative product components that incorporate self-distance corrections, we develop a multiplicative hybrid contraction mapping. We show that, under suitable conditions on the contractive coefficients and exponents, such mappings admit a fixed point in both classes of complete spaces. To validate the theoretical results, we provide illustrative numerical examples. Finally, we apply our fixed point theorem to establish the existence of solutions for a class of nonlinear Volterra-type integral equations with variable delays and weakly singular kernels.