Fixed point theorem for discontinuous mappings on PN spaces

TL;DR

This paper develops a fixed point theorem for discontinuous mappings in probabilistic normed spaces using measures of discontinuity, expanding fixed point theory in probabilistic functional analysis.

Contribution

Introduces a fixed point theorem for discontinuous mappings on PN spaces utilizing measure of discontinuity, advancing the understanding of fixed points in probabilistic spaces.

Findings

Established a fixed point theorem for discontinuous mappings on PN spaces.

Analyzed strong t-continuity and measure of discontinuity in PN spaces.

Applied the theorem to specific self mappings in probabilistic normed spaces.

Abstract

We present a study on strong t-continuity and measure of discontinuity on PN spaces. As an application, we prove a fixed point theorem for a self mapping on PN spaces by means of measure of discontinuity.