Nonunique Fixed-Point Results in a General Setting With an Application

Abstract

This manuscript's main goal is to examine the presence of fixed points in the context of controlled metric-type spaces utilizing rational type & Cacute;iri & cacute;-contractive conditions. We provide appropriate examples to support the validity and superiority of our conclusions. In the context of extended b-metric space, b-metric spaces, and standard metric spaces, our findings extrapolate and expand a number of well-known research findings. As an application of our findings, we prove that a second-order differential equation has a solution. The paper ends with a few open problems for further investigation of additional dimensions within this framework.