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), 2022. Published by Science Publishing Group

Keywords

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

References

[1]	Aydi, H, Monica, Felicia, Bota, M, Karapinar, E and Mitrović, S (2012) “A fixed point theorem for set-valued quasi contractions in b-metric spaces”, Fixed Point Theory and Application no. 88.
[2]	Achari J. (1983): “Fixed point theorems for a class of mappings on non-Archimedean probabilistic metric spaces, Mathematica, 25, 5-9.
[3]	Amit Singh, Sandeep Bhatt, Shruti Charkiyal,(2011)“A unique common fixed point theorem for four maps in non-Archimedean Menger PM-spaces”, Int. Journal of Math. Analysis, Vol. 5 (15), 705-712.
[4]	Alamgir Khan M, Sumitra (2008) “Common fixed point theorem in 2 N. A. Menger PM space for R-weakly commuting maps of type (P)”, Novi Sad J. Math. (38) (2), 145-152.
[5]	Alamgir Khan M Sumitra: “A common fixed point theorem in non-ArchimedeanMenger PM-space”, Novi Sad J. Math., Vol. 39 (2), 81-87.2009.
[6]	Alamgir Khan M and Sumitra: “Common fixed point theorems in non-ArchideanMenge PM-space”, 5 (1), 1-13, 2010.
[7]	Bota, M, Molnar, A and Varga, C: “On ekeland's variational principle in b-metric spaces”, Fixed Point Theory no. 2, 21-28, 12 (2011).
[8]	Chugh, Rkumar, V, and Kadian, T:: Some fixed point theorems for multivalued mappings in generalized b-metric spaces, International Journal of Mathematical Archive, no. 3, 1198-1210, 3 (2012).
[9]	Czerwik, S: “Contraction mappings in b-metric spaces”, Acta Mathematica et Informatica Universitatis Ostraviensis, 5-11. 1 (1993).
[10]	Czerwik S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti. Sem. Mat. Fis. Univ. Modena 46 (1998), 263-276.
[11]	J. R. Morales and E. Rojas: “Cone metric spaces and fixed point theorems of T –Kannan contractive mappings” arXiv: 0907. 3949v2 [math. FA] 26 Oct. 2009.
[12]	Kir, M, Kiziltunc, H: “On some well-known fixed point theorems in b-metric spaces”, Turkish Journal of Analysis and Number Theory, 1, no. 1, 13-16. (2013).
[13]	Khan, M. S: “A fixed point theorem for metric spaces”, Rent. Inst. Mat. Univ. Trieste, Vol. III, Fasc. 10 1 – 4. (1976).
[14]	L. G. Haung and X. Zhang: “Cone metric spaces and fixed point of contractive mapping”, J. Math. Anal.
[15]	M. Jleli, B. Samet, The Kannan’s fixed point theorem in a cone rectangular metric space, J. Nonlinear Sci. Appl. 2 (3) (2009), 161–167. 2009.
[16]	N. Shioji, T. Suzuki and W. Takahashi: “Contraction mappings, Kannan mappings and metric completeness” Proceedings of the American Mathematical Society, vol. 126, No. 10, 3117-3124, October 1998.
[17]	R. George, Hossam A. Nabwey, K. P. Reshma and R. Rajagopalan: "generalized cone b-metric spaces and contraction principles" MATEMATIQKI VESNIK, 67, 4 (2015), 246–257, December 2015.
[18]	R. George, B. Fisher, "Some generalized results of fixed points in cone b-metric space", Math. Moravica 17 (2) (2013), 39–50., 2013.
[19]	S. Rezapour and R. Hamibarani: “Some notes on the paper Cone metric spaces and fixed point Theorems of contractive mappings” J. Math. Anal. Appl., 345, (2), 719-724, 2008.
[20]	Shi, L, Xu, S: “Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces”, Fixed Point Theory and Applications, no. 120. 2013.
[21]	S. Moradi: “Kannan fixed point theorem on complete metric spaces and on generalized metric spaces depend on another function” arXiv: 0903, 1577v1 [math. FA].
[22]	T. Suzuki, "Generalized metric spaces do not have compatible topology", Abstract Appl. Anal. 2014, Art. ID 458098, 5 pages.
[23]	T. Van An, N. Van Dung, Z. Kadelburg, S. Radenovi´c, "Various generalizations of metric spaces and fixed point theorem"s, Rev. Real Acad. Cienc. Exac., Fis. Nat., Ser. A, Mat. 109, 1 (2015), 175–198.
[24]	Z. Kadelburg, S. Radenovi´c, Fixed point results in generalized metric spaces without Hausdorff property, Math. Sci. 8: 125 (2014).

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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