Some new results in Menger PbM-spaces for single-valued and multi-valued mappings via simulation functions with its application

The main goal of the present paper is to obtain several fixed point theorems for both multi-valued and single-valued mappings in Menger PbM-spaces, which is an extension of Menger PM-spaces. In this paper, we introduce different types of contractive mappings by introducing the notions of (\alpha-\psi)-E-type simulation function and (\beta-\psi)-E-type simulation function in Menger PbM-spaces which is a generalization of simulation functions introduced by Khojasteh. Furthermore, we present some nontrivial examples and an application to the existence of a solution of the Volterra-type integral equation.

کلیدواژه ها:

Menger PbM-spaces ، simulation function ، self mappings ، orbital admissible mappings ، Multi-valued mapping