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.
Original language | English |
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Pages (from-to) | 9493-9507 |
Number of pages | 15 |
Journal | AIMS Mathematics |
Volume | 7 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2022 |
Externally published | Yes |
Keywords
- Banach algebra A
- Fixed point
- Fuzzy metric space over A
- Integral equation