International Journal of Nonlinear Analysis and Applications

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

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran

10.22075/ijnaa.2022.27258.3681

Abstract

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.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 25 November 2024
  • Receive Date: 03 July 2022
  • Revise Date: 20 September 2022
  • Accept Date: 27 September 2022