Hybrid coincidence and common fixed point theorems in Menger probabilistic metric spaces under a strict contractive condition with an application

Abstract

We prove some coincidence and common fixed point theorems for two hybrid pairs of mappings in Menger spaces satisfying a strict contractive condition. An illustrative example is given to support the genuineness of our extension, besides deriving some related results. Then, we establish the corresponding common fixed point theorems in metric spaces. Finally, we utilize our main result to obtain the existence of a common solution for a system of Volterra type integral equations.