Minimization Theorem and Fixed-Point Theorem in Probabilistic Metric Space

Authors

  • Akhilesh Jain Department of Mathematics, Corporate Institute of Science and Technology, Bhopal, Madhya Pradesh
  • R. S. Chandel Department of Mathematics, Government Geetanjali Girls P.G. College, Bhopal, Madhya Pradesh
  • Manoj Sharma Department of Mathematics, Sagar Institute of Research and Technology, Bhopal, Madhya Pradesh
  • Uday Dolas Department of Mathematics, Chandra Shekhar Azad Government P.G. College, Sehore, Madhya Pradesh

DOI:

https://doi.org/10.37628/jsmfe.v5i2.937

Keywords:

common fixed point, generating space of quasi-probabilistic metric family, minimization theorem, quasi-compatible mapping, quasi-metric space

Abstract

This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper, the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces, Menger PM-spaces and probabilistic normed linear spaces (PN-space) are given, and the characterizations of various probabilistically bounded sets are presented. As applications, we utilize these results obtained in this paper to study the linear operator theory and fixed-point theory on PM-spaces. In this paper, we prove minimization theorem in the generating space of quasi-probabilistic metric space. Also, we prove common fixed-point theorem for the space which satisfies the minimization theorem.

Downloads

Published

2019-10-04

Issue

Vol. 5 No. 2 (2019)

Section

Articles