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

Saif Ur Rehman; Arjamand Bano; Hassen Aydi; Choonkil Park

doi:10.3934/math.2022527

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

Saif Ur Rehman, Arjamand Bano, Hassen Aydi^*, Choonkil Park^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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
Pages (from-to)	9493-9507
Number of pages	15
Journal	AIMS Mathematics
Volume	7
Issue number	5
DOIs	https://doi.org/10.3934/math.2022527
Publication status	Published - 2022
Externally published	Yes

Keywords

Banach algebra A
Fixed point
Fuzzy metric space over A
Integral equation

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10.3934/math.2022527

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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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AU - Aydi, Hassen

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Y1 - 2022

N2 - 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.

AB - 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.

KW - Banach algebra A

KW - Fixed point

KW - Fuzzy metric space over A

KW - Integral equation

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JF - AIMS Mathematics

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ER -

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

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Keywords

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