Some Fixed Point Theorems on b<sub>2</sub> - Metric Spaces

Bheem Singh Patel; Zaheer Kareem Ansari; Dharmendra Kumar; Arun Garg

doi:doi:10.11648/j.pamj.20231204.12

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Some Fixed Point Theorems on b₂ - Metric Spaces

Bheem Singh Patel, Zaheer Kareem Ansari, Dharmendra Kumar, Arun Garg

Published in Pure and Applied Mathematics Journal (Volume 12, Issue 4)

Received: 25 August 2023 Accepted: 14 September 2023 Published: 27 September 2023

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Abstract

In this study, we generalize both b-metric spaces and 2-metric spaces into a new class of generalized metric spaces that we call b₂-metric spaces. Then, under various contractive circumstances in partially ordered spaces, we demonstrate a few fixed point theorems in b₂-metric space. Many Mathematician gave the concept of b₂ -metric spaces as a generalization of 2-metric space. The purpose of this research article to established some results of 2-metric space proved by the Arun Garg et al. in b₂ -metric spaces and prove new results.

Published in	Pure and Applied Mathematics Journal (Volume 12, Issue 4)
DOI	10.11648/j.pamj.20231204.12
Page(s)	72-78
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fixed Point, b - Metric Space, 2-Metric Space, Partial Order Set, Generalized Contractive Mappings

References

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APA Style

Bheem Singh Patel, Zaheer Kareem Ansari, Dharmendra Kumar, Arun Garg. (2023). Some Fixed Point Theorems on b2 - Metric Spaces. Pure and Applied Mathematics Journal, 12(4), 72-78. https://doi.org/10.11648/j.pamj.20231204.12

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ACS Style

Bheem Singh Patel; Zaheer Kareem Ansari; Dharmendra Kumar; Arun Garg. Some Fixed Point Theorems on b2 - Metric Spaces. Pure Appl. Math. J. 2023, 12(4), 72-78. doi: 10.11648/j.pamj.20231204.12

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AMA Style

Bheem Singh Patel, Zaheer Kareem Ansari, Dharmendra Kumar, Arun Garg. Some Fixed Point Theorems on b2 - Metric Spaces. Pure Appl Math J. 2023;12(4):72-78. doi: 10.11648/j.pamj.20231204.12

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@article{10.11648/j.pamj.20231204.12,
  author = {Bheem Singh Patel and Zaheer Kareem Ansari and Dharmendra Kumar and Arun Garg},
  title = {Some Fixed Point Theorems on b2 - Metric Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {12},
  number = {4},
  pages = {72-78},
  doi = {10.11648/j.pamj.20231204.12},
  url = {https://doi.org/10.11648/j.pamj.20231204.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20231204.12},
  abstract = {In this study, we generalize both b-metric spaces and 2-metric spaces into a new class of generalized metric spaces that we call b2-metric spaces. Then, under various contractive circumstances in partially ordered spaces, we demonstrate a few fixed point theorems in b2-metric space. Many Mathematician gave the concept of b2 -metric spaces as a generalization of 2-metric space. The purpose of this research article to established some results of 2-metric space proved by the Arun Garg et al. in b2 -metric spaces and prove new results.},
 year = {2023}
}

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TY  - JOUR
T1  - Some Fixed Point Theorems on b2 - Metric Spaces
AU  - Bheem Singh Patel
AU  - Zaheer Kareem Ansari
AU  - Dharmendra Kumar
AU  - Arun Garg
Y1  - 2023/09/27
PY  - 2023
N1  - https://doi.org/10.11648/j.pamj.20231204.12
DO  - 10.11648/j.pamj.20231204.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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PB  - Science Publishing Group
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AB  - In this study, we generalize both b-metric spaces and 2-metric spaces into a new class of generalized metric spaces that we call b2-metric spaces. Then, under various contractive circumstances in partially ordered spaces, we demonstrate a few fixed point theorems in b2-metric space. Many Mathematician gave the concept of b2 -metric spaces as a generalization of 2-metric space. The purpose of this research article to established some results of 2-metric space proved by the Arun Garg et al. in b2 -metric spaces and prove new results.
VL  - 12
IS  - 4
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Author Information

Bheem Singh Patel

Department of Mathematics, Madhyanchal Professional University, Bhopal, India
Zaheer Kareem Ansari

Department of Mathematics, JSS Academy of Technical Education, Noida, India
Dharmendra Kumar

Department of Mathematics Satyawati College (Evening), University of Delhi, Delhi, India
Arun Garg

Department of Mathematics, Madhyanchal Professional University, Bhopal, India

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APA Style

Bheem Singh Patel, Zaheer Kareem Ansari, Dharmendra Kumar, Arun Garg. (2023). Some Fixed Point Theorems on b2 - Metric Spaces. Pure and Applied Mathematics Journal, 12(4), 72-78. https://doi.org/10.11648/j.pamj.20231204.12

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ACS Style

Bheem Singh Patel; Zaheer Kareem Ansari; Dharmendra Kumar; Arun Garg. Some Fixed Point Theorems on b2 - Metric Spaces. Pure Appl. Math. J. 2023, 12(4), 72-78. doi: 10.11648/j.pamj.20231204.12

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AMA Style

Bheem Singh Patel, Zaheer Kareem Ansari, Dharmendra Kumar, Arun Garg. Some Fixed Point Theorems on b2 - Metric Spaces. Pure Appl Math J. 2023;12(4):72-78. doi: 10.11648/j.pamj.20231204.12

Copy | Download

@article{10.11648/j.pamj.20231204.12,
  author = {Bheem Singh Patel and Zaheer Kareem Ansari and Dharmendra Kumar and Arun Garg},
  title = {Some Fixed Point Theorems on b2 - Metric Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {12},
  number = {4},
  pages = {72-78},
  doi = {10.11648/j.pamj.20231204.12},
  url = {https://doi.org/10.11648/j.pamj.20231204.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20231204.12},
  abstract = {In this study, we generalize both b-metric spaces and 2-metric spaces into a new class of generalized metric spaces that we call b2-metric spaces. Then, under various contractive circumstances in partially ordered spaces, we demonstrate a few fixed point theorems in b2-metric space. Many Mathematician gave the concept of b2 -metric spaces as a generalization of 2-metric space. The purpose of this research article to established some results of 2-metric space proved by the Arun Garg et al. in b2 -metric spaces and prove new results.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Some Fixed Point Theorems on b2 - Metric Spaces
AU  - Bheem Singh Patel
AU  - Zaheer Kareem Ansari
AU  - Dharmendra Kumar
AU  - Arun Garg
Y1  - 2023/09/27
PY  - 2023
N1  - https://doi.org/10.11648/j.pamj.20231204.12
DO  - 10.11648/j.pamj.20231204.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 72
EP  - 78
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20231204.12
AB  - In this study, we generalize both b-metric spaces and 2-metric spaces into a new class of generalized metric spaces that we call b2-metric spaces. Then, under various contractive circumstances in partially ordered spaces, we demonstrate a few fixed point theorems in b2-metric space. Many Mathematician gave the concept of b2 -metric spaces as a generalization of 2-metric space. The purpose of this research article to established some results of 2-metric space proved by the Arun Garg et al. in b2 -metric spaces and prove new results.
VL  - 12
IS  - 4
ER  -

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