Open AccessAn approach of Banach algebra in fuzzy metric spaces with an application
Author(s) -
Saif Ur Rehman,
Arjamand Bano,
Hassen Aydi,
Choonkil Park
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022527
Subject(s) - mathematics , banach algebra , banach manifold , hausdorff space , pure mathematics , banach space , discrete mathematics , algebra over a field , lp space
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 $ \mathcal{A} $ is an open set. We present some more topological properties and a Hausdorff metric on FM-spaces over $ \mathcal{A} $. Moreover, we state and prove a fuzzy Banach contraction theorem on FM-spaces over a Banach algebra $ \mathcal{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.