Fixed point theorems for multivalued and single-valued contractive mappings on Menger PM spaces with applications

In this paper, by introducing multivalued (α,η)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha ,\eta )$$\end{document}–ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-contractive mappings, we obtain new fixed point theorems for multivalued and single-valued mappings and also coupled fixed point theorems in complete Menger PM and partially ordered Menger PM spaces. We have improved, extended and generalized probabilistic version of the very important generalization of the Banach contraction principle. Some examples and also application of our results in metric spaces and an application to existence of solution of Volterra-type integral equation are given to support the obtained results.