AIMS Mathematics (Mar 2022)

An approach of Banach algebra in fuzzy metric spaces with an application

  • Saif Ur Rehman,
  • Arjamand Bano,
  • Hassen Aydi ,
  • Choonkil Park

DOI
https://doi.org/10.3934/math.2022527
Journal volume & issue
Vol. 7, no. 5
pp. 9493 – 9507

Abstract

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The purpose of this paper is to present a new concept of a Banach algebra in a fuzzy metric space (FM-space). We define an open ball, an open set and prove that every open ball in an FM-space over a Banach algebra A is an open set. We present some more topological properties and a Hausdorff metric on FM-spaces over A. Moreover, we state and prove a fuzzy Banach contraction theorem on FM-spaces over a Banach algebra A. Furthermore, we present an application of an integral equation and will prove a result dealing with the integral operators in FM-spaces over a Banach algebra.

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