$ N_b $-fuzzy metric spaces with topological properties and applications

Jerolina Fernandez; Hüseyin Işık; Neeraj Malviya; Fahd Jarad; Jerolina Fernandez; Hüseyin Işık; Neeraj Malviya; Fahd Jarad

doi:10.3934/math.2023296

AIMS Mathematics

2023, Volume 8, Issue 3: 5879-5898. doi: 10.3934/math.2023296

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Research article

$ N_b $-fuzzy metric spaces with topological properties and applications

1.
Department of Mathematics & Statistics, The Bhopal School of Social Sciences, Bhopal, M.P., India
2.
Department of Engineering Science, Bandırma Onyedi Eylül University, Bandırma 10200, Balıkesir, Turkey
3.
Department of Mathematics, Government College, Timarni, M.P., India
4.
Department of Mathematics, Cankaya University, Etimesgut 06790, Ankara, Turkey
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Received: 08 August 2022 Revised: 17 November 2022 Accepted: 22 November 2022 Published: 26 December 2022
MSC : 47H10, 54A40, 54E35, 54E40, 54H25

Our aim is to introduce the notion of $ N_{b} $-fuzzy metric space (FMS). We also define quasi $ N $-FMS, and pseudo $ N_{b} $-FMS with examples and counterexamples and prove a decomposition theorem for pseudo $ N_{b} $-FMS. We prove various theorems related to the convergence of sequences and analyze topology of symmetric $ N_{b} $-FMS. At last, we provide an application of $ q $-contraction mapping as a Banach contraction principle (BCP) in the structure of symmetric $ N_{b} $-FMS and applied it in the solution of integral equations and linear equations.
- $ N_{b} $-fuzzy metric space,
- pseudo $ N_{b} $-fuzzy metric space,
- quasi $ N $-fuzzy metric space,
- q-contraction
Citation: Jerolina Fernandez, Hüseyin Işık, Neeraj Malviya, Fahd Jarad. $ N_b $-fuzzy metric spaces with topological properties and applications[J]. AIMS Mathematics, 2023, 8(3): 5879-5898. doi: 10.3934/math.2023296

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Abstract

Our aim is to introduce the notion of $ N_{b} $-fuzzy metric space (FMS). We also define quasi $ N $-FMS, and pseudo $ N_{b} $-FMS with examples and counterexamples and prove a decomposition theorem for pseudo $ N_{b} $-FMS. We prove various theorems related to the convergence of sequences and analyze topology of symmetric $ N_{b} $-FMS. At last, we provide an application of $ q $-contraction mapping as a Banach contraction principle (BCP) in the structure of symmetric $ N_{b} $-FMS and applied it in the solution of integral equations and linear equations.

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