An approach of Banach algebra in fuzzy metric spaces with an applicationopen access
- Authors
- Rehman, Saif Ur; Bano, Arjamand; Aydi, Hassen; Park, Choonkil
- Issue Date
- Mar-2022
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- fixed point; Banach algebra A; fuzzy metric space over A; integral equation
- Citation
- AIMS MATHEMATICS, v.7, no.5, pp.9493 - 9507
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS MATHEMATICS
- Volume
- 7
- Number
- 5
- Start Page
- 9493
- End Page
- 9507
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/139086
- DOI
- 10.3934/math.2022527
- Abstract
- 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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