Modular Cone Metric Spaces

Saeedeh Shamsi Gamchi; Asadollah Niknam

doi:doi:10.11648/j.pamj.20130206.14

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Modular Cone Metric Spaces

Saeedeh Shamsi Gamchi, Asadollah Niknam

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 6)

Received: 31 December 2013 Published: 30 January 2014

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Abstract

In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces, Fixed Point Theory Appl. (2011)" is not true.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 6)
DOI	10.11648/j.pamj.20130206.14
Page(s)	191-196
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), 2014. Published by Science Publishing Group

Keywords

Ordered Spaces, Modular Cone Metric, Fixed Point Theorem

References

[1]	H. Cakalli, A. Sonmez, C. Genc, On an equivalence of topological vector space valued cone metric spaces and metric spaces.Appl. Math. Lett. 25 (2012) 429-433.
[2]	G.Y. Chen, X.X. Huang,X.Q. Yang,Vector Optimization.Springer-Verlag, Berlin, Heidelberg. (2005).
[3]	V. Chistyakov, A fixed point theorem for contractions in modular metric spaces.arXiv: 1112.5561v1. (2011)
[4]	V. Chistyakov, Metric modulars and their application. Dokl.Math. 73 (1)(2006) 32-35.
[5]	V. Chistyakov, Modular metric spaces generated by F-modulars, Folia Math‎.‎14‎ (2008)‎ 3-25.
[6]	V. Chistyakov, Modular metric spaces, I: Basic concepts. Nonlinear Anal.72 (2010) 1-14.
[7]	K. Deimling,Nonlinear Functional Analysis. Springer-Verlag, Berlin. (1985).
[8]	W.S. Du,A note on cone metric fixed point theory and it’s equivalence.Nonlinear Anal. 72. (2010)2259-2261.
[9]	S. Jankovic, Z.Golubovic,S. Radenovic,Compatible and weakly compatible mappings in cone metric spaces.Math. Comp.Modelling. 52(2010) 1728-1738.
[10]	Ch. Mongkolkeha, W. Sintunavarat,P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces.Fixed Point Theory Appl. (2011)
[11]	H. Nakano, Modulared Semi-Ordered Linear Spaces.In Tokyo Math Book Ser, vol. 1. Maruzen Co., Tokyo. (1950).
[12]	B. Rzepecki,On fixed point theorems of Maia type.Publications de l’InstitutMathématique,28 (42)(1980) 179-186.
[13]	J. Musielak, W. Orlicz, On modular spaces.Studia Math. 18 (1959)591-597.

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Saeedeh Shamsi Gamchi, Asadollah Niknam. (2014). Modular Cone Metric Spaces. Pure and Applied Mathematics Journal, 2(6), 191-196. https://doi.org/10.11648/j.pamj.20130206.14

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ACS Style

Saeedeh Shamsi Gamchi; Asadollah Niknam. Modular Cone Metric Spaces. Pure Appl. Math. J. 2014, 2(6), 191-196. doi: 10.11648/j.pamj.20130206.14

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AMA Style

Saeedeh Shamsi Gamchi, Asadollah Niknam. Modular Cone Metric Spaces. Pure Appl Math J. 2014;2(6):191-196. doi: 10.11648/j.pamj.20130206.14

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@article{10.11648/j.pamj.20130206.14,
  author = {Saeedeh Shamsi Gamchi and Asadollah Niknam},
  title = {Modular Cone Metric Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {6},
  pages = {191-196},
  doi = {10.11648/j.pamj.20130206.14},
  url = {https://doi.org/10.11648/j.pamj.20130206.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130206.14},
  abstract = {In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces, Fixed Point Theory Appl. (2011)" is not true.},
 year = {2014}
}

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TY  - JOUR
T1  - Modular Cone Metric Spaces
AU  - Saeedeh Shamsi Gamchi
AU  - Asadollah Niknam
Y1  - 2014/01/30
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20130206.14
DO  - 10.11648/j.pamj.20130206.14
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 191
EP  - 196
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130206.14
AB  - In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces, Fixed Point Theory Appl. (2011)" is not true.
VL  - 2
IS  - 6
ER  -

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Author Information

Saeedeh Shamsi Gamchi

Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran
Asadollah Niknam

Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran

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Saeedeh Shamsi Gamchi, Asadollah Niknam. (2014). Modular Cone Metric Spaces. Pure and Applied Mathematics Journal, 2(6), 191-196. https://doi.org/10.11648/j.pamj.20130206.14

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ACS Style

Saeedeh Shamsi Gamchi; Asadollah Niknam. Modular Cone Metric Spaces. Pure Appl. Math. J. 2014, 2(6), 191-196. doi: 10.11648/j.pamj.20130206.14

Copy | Download

AMA Style

Saeedeh Shamsi Gamchi, Asadollah Niknam. Modular Cone Metric Spaces. Pure Appl Math J. 2014;2(6):191-196. doi: 10.11648/j.pamj.20130206.14

Copy | Download

@article{10.11648/j.pamj.20130206.14,
  author = {Saeedeh Shamsi Gamchi and Asadollah Niknam},
  title = {Modular Cone Metric Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {6},
  pages = {191-196},
  doi = {10.11648/j.pamj.20130206.14},
  url = {https://doi.org/10.11648/j.pamj.20130206.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130206.14},
  abstract = {In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces, Fixed Point Theory Appl. (2011)" is not true.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Modular Cone Metric Spaces
AU  - Saeedeh Shamsi Gamchi
AU  - Asadollah Niknam
Y1  - 2014/01/30
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20130206.14
DO  - 10.11648/j.pamj.20130206.14
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 191
EP  - 196
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130206.14
AB  - In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces, Fixed Point Theory Appl. (2011)" is not true.
VL  - 2
IS  - 6
ER  -

Copy | Download