فهرست نشریات علمی دسترسی آزاد ایران

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.