Parametric metric spaces and integral-type contractions: new fixed point theorems with applications

Abstract

In this article, we establish new fixed point theorems for self-mappings defined on complete parametric metric spaces. By introducing a generalized integral-type contractive condition involving an auxiliary control function. The approach relies on the concept of convergence and completeness in parametric settings, which naturally generalizes classical metric frameworks. As an application, we demonstrate the existence of solutions to nonlinear integral equations, highlighting the applicability of the proposed framework. Several examples are presented to illustrate the effectiveness and novelty of the obtained results.