The nonlinear contraction in probabilistic cone b-metric spaces with application to integral equation

Abstract

The probabilistic cone b-metric space is a novel concept that we describe in this study along with some of its fundamental topological properties and instances. We also established the fixed point theorem for the probabilistic nonlinear Banach contraction mapping on this kind of spaces. Many prior findings in the literature are generalized and unified by our findings. In order to illustrate the basic theorem in ordinary cone b-metric spaces, some related findings are also provided with an application to integral equation.

Keywords

• probabilistic cone b-metric spaces
• fixed point
• phi-contraction
• integral equation