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

Nazmul, Sk; Badyakar, Utpal

doi:10.21608/ejmaa.2024.297057.1223

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

Document Type : Regular research papers

Authors

Sk Nazmul ¹
Utpal Badyakar ²

¹ Department of Mathematics, Kazi Nazrul University, Asansol-713340, India

² Department of Mathematics, Bankura Sammilani College, Bankura-722102, India

10.21608/ejmaa.2024.297057.1223

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.

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