Fixed Point Result on Generalized Cone b-Metric Spaces

Zaheer Kareem Ansari; Ajay Kumar Singh; Pawan Kumar; Jay Prakash Patel

doi:doi:10.11648/j.pamj.20221102.11

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Fixed Point Result on Generalized Cone b-Metric Spaces

Zaheer Kareem Ansari, Ajay Kumar Singh, Pawan Kumar, Jay Prakash Patel

Published in Pure and Applied Mathematics Journal (Volume 11, Issue 2)

Received: 8 February 2022 Accepted: 10 March 2022 Published: 31 March 2022

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Abstract

The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George et al. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.

Published in	Pure and Applied Mathematics Journal (Volume 11, Issue 2)
DOI	10.11648/j.pamj.20221102.11
Page(s)	28-32
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

Metric Space, b-metric Space, Cone Metric Space, Cone b-metric Space, Rectangular Metric Space

References

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APA Style

Zaheer Kareem Ansari, Ajay Kumar Singh, Pawan Kumar, Jay Prakash Patel. (2022). Fixed Point Result on Generalized Cone b-Metric Spaces. Pure and Applied Mathematics Journal, 11(2), 28-32. https://doi.org/10.11648/j.pamj.20221102.11

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ACS Style

Zaheer Kareem Ansari; Ajay Kumar Singh; Pawan Kumar; Jay Prakash Patel. Fixed Point Result on Generalized Cone b-Metric Spaces. Pure Appl. Math. J. 2022, 11(2), 28-32. doi: 10.11648/j.pamj.20221102.11

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AMA Style

Zaheer Kareem Ansari, Ajay Kumar Singh, Pawan Kumar, Jay Prakash Patel. Fixed Point Result on Generalized Cone b-Metric Spaces. Pure Appl Math J. 2022;11(2):28-32. doi: 10.11648/j.pamj.20221102.11

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@article{10.11648/j.pamj.20221102.11,
  author = {Zaheer Kareem Ansari and Ajay Kumar Singh and Pawan Kumar and Jay Prakash Patel},
  title = {Fixed Point Result on Generalized Cone b-Metric Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {11},
  number = {2},
  pages = {28-32},
  doi = {10.11648/j.pamj.20221102.11},
  url = {https://doi.org/10.11648/j.pamj.20221102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221102.11},
  abstract = {The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George et al. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.},
 year = {2022}
}

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TY  - JOUR
T1  - Fixed Point Result on Generalized Cone b-Metric Spaces
AU  - Zaheer Kareem Ansari
AU  - Ajay Kumar Singh
AU  - Pawan Kumar
AU  - Jay Prakash Patel
Y1  - 2022/03/31
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221102.11
DO  - 10.11648/j.pamj.20221102.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 28
EP  - 32
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20221102.11
AB  - The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George et al. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.
VL  - 11
IS  - 2
ER  -

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Author Information

Zaheer Kareem Ansari

Department of Mathematics, JSS Academy of Technical Education, Noida, India
Ajay Kumar Singh

Department of Mathematics, Madhyanchal Professional University, Bhopal, India
Pawan Kumar

Department of Mathematics, Maitreyi College, University of Delhi, Chanakyapuri, New Delhi, India
Jay Prakash Patel

Department of Mathematics, Madhyanchal Professional University, Bhopal, India

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APA Style

Zaheer Kareem Ansari, Ajay Kumar Singh, Pawan Kumar, Jay Prakash Patel. (2022). Fixed Point Result on Generalized Cone b-Metric Spaces. Pure and Applied Mathematics Journal, 11(2), 28-32. https://doi.org/10.11648/j.pamj.20221102.11

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ACS Style

Zaheer Kareem Ansari; Ajay Kumar Singh; Pawan Kumar; Jay Prakash Patel. Fixed Point Result on Generalized Cone b-Metric Spaces. Pure Appl. Math. J. 2022, 11(2), 28-32. doi: 10.11648/j.pamj.20221102.11

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AMA Style

Zaheer Kareem Ansari, Ajay Kumar Singh, Pawan Kumar, Jay Prakash Patel. Fixed Point Result on Generalized Cone b-Metric Spaces. Pure Appl Math J. 2022;11(2):28-32. doi: 10.11648/j.pamj.20221102.11

Copy | Download

@article{10.11648/j.pamj.20221102.11,
  author = {Zaheer Kareem Ansari and Ajay Kumar Singh and Pawan Kumar and Jay Prakash Patel},
  title = {Fixed Point Result on Generalized Cone b-Metric Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {11},
  number = {2},
  pages = {28-32},
  doi = {10.11648/j.pamj.20221102.11},
  url = {https://doi.org/10.11648/j.pamj.20221102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221102.11},
  abstract = {The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George et al. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Fixed Point Result on Generalized Cone b-Metric Spaces
AU  - Zaheer Kareem Ansari
AU  - Ajay Kumar Singh
AU  - Pawan Kumar
AU  - Jay Prakash Patel
Y1  - 2022/03/31
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221102.11
DO  - 10.11648/j.pamj.20221102.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 28
EP  - 32
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20221102.11
AB  - The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George et al. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.
VL  - 11
IS  - 2
ER  -

Copy | Download