Some Fixed Point Theorems in Menger Probabilistic Partial Metric Spaces with Application to Volterra Type Integral Equation

Abstract

In this paper, we introduce the notion of Menger probabilistic partial metric space and prove some fixed point theorems in the framework of such spaces. Some examples and an application to Volterra type integral equation are given to support the obtained results. Finally, we apply successive approximations method to find a solution for a Volterra type integral equation with high accuracy.