Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces

Abstract

We introduce the concepts of $(H,\psi ,\mathrm{\Phi })$-contraction and probabilistic $(\alpha ,\phi )$-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.