420168

Generalized Soft b -Metric Spaces and Some of its Fixed Soft Point Results

Article

Last updated: 09 Apr 2025

Subjects

-

Tags

Functional analysis

Abstract

In the present paper, our main aim is to develop the fixed point results of b -Metric Spaces in a soft set setting. To accomplish this, we first redefined Wadkar et al.'s soft b -Metric Space, renaming it ``Generalized soft b -Metric Space with soft real number $\widetilde{b}~ (~\widetilde{\ge} ~\overline{1}~)"$ and demonstrating a non-trivial example. Afterward, some basic concepts in generalized soft b -Metric Spaces such as Cauchy sequence, convergence, completeness etc. are redefined and justified with proper examples. Finally, we established some important fixed soft point results using soft mapping in generalized soft b -Metric Spaces.

In 2019, Abbas et al. proved a result (Theorem 6.3) on Soft b -Metric Spaces by using a finite set of parameters, but in the proof there is no use of the finiteness property, although they showed the importance of the finiteness property by an example.

Accordingly, we have shown the importance of finiteness in the proof. For this reason, we modified the soft b -Metric Space definition, renamed it ``Generalized Soft b -Metric Spaces", and verified it with a non-trivial example. Afterwards, in this metric space, some basic characteristics of the Cauchy sequence and its completeness with proper examples are investigated. Finally, using soft mapping, some celebrated fixed soft point results are established in generalized soft b -Metric Spaces. Theorem 6.3 can be proved by using generalized soft b -metric spaces.

DOI

10.21608/ejmaa.2024.297057.1223

Keywords

soft set, soft point, soft mapping, Generalized Soft $b$ -Metric Space, fixed soft point

Authors

First Name

Sk

Last Name

Nazmul

MiddleName

-

Affiliation

Department of Mathematics, Kazi Nazrul University, Asansol-713340, India

Email

sk.nazmul_math@yahoo.in

City

Asansol

Orcid

0000-0001-6674-1459

First Name

Utpal

Last Name

Badyakar

MiddleName

-

Affiliation

Department of Mathematics, Bankura Sammilani College, Bankura-722102, India

Email

ubmath16@gmail.com

City

Bankura

Orcid

0000-0002-6397-4924

Volume

13

Article Issue

1

Related Issue

51150

Issue Date

2025-01-01

Receive Date

2024-06-12

Publish Date

2025-01-01

Page Start

1

Page End

11

Print ISSN

3009-6731

Online ISSN

2090-729X

Link

https://ejmaa.journals.ekb.eg/article_420168.html

Detail API

http://journals.ekb.eg?_action=service&article_code=420168

Order

420,168

Type

Regular research papers

Type Code

2,651

Publication Type

Journal

Publication Title

Electronic Journal of Mathematical Analysis and Applications

Publication Link

https://ejmaa.journals.ekb.eg/

MainTitle

Generalized Soft b -Metric Spaces and Some of its Fixed Soft Point Results

Details

Type

Article

Created At

09 Apr 2025