An Extension of a Fixed Point Result in Cone Banach Space

Elvin Rada; Agron Tato

doi:doi:10.11648/j.pamj.20150403.12

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An Extension of a Fixed Point Result in Cone Banach Space

Elvin Rada, Agron Tato

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3)

Received: 3 April 2015 Accepted: 14 April 2015 Published: 24 April 2015

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Abstract

In this paper we study a class of mappings in a ConeBanach Space which have at least one fixed point. More precisely for a closed and convex subset C of a cone Banach space with a generalized norm that satisfy a special condition. We are proposing some extensions of the results of Karapinar.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 3)
DOI	10.11648/j.pamj.20150403.12
Page(s)	70-74
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), 2015. Published by Science Publishing Group

Keywords

Fixed Point, Contraction, Cone Banach Space

References

[1]	Rzepecki, B., “On fixed point theorems of Maia type,” Publications de l’InstitutMath´ematique, vol. 28_42_, pp. 179–186, 1980.
[2]	Maia, M.G., “Un’osservazionesullecontrazionimetriche,” RendicontidelSeminarioMatematicodellaUniversit`a di Padova, vol. 40, pp. 139–143, 1968.
[3]	Lin, S. D., “A common fixed point theorem in abstract space” Indian Journal of Pure and Applied Mathematics. Vol. 18, no.8, pp. 685-690.1987
[4]	Huang L,-G., Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings,”Journal of Mathematical Analysis and Applications, vol. 332, no. 2, pp. 1468–1476, 2007
[5]	Karapinar, E., Fixed point theorems in Cone Banach Spaces. Hindawi Publishing Company. Vol. 2009.Article ID 609281, 9 pages.
[6]	Rezapour Sh., and Hamlbarani, R., “Some notes on the paper: “Cone metric spaces and fixed point theorems of contractive mappings”,” Journal of Mathematical Analysis and Applications, vol. 345, no. 2, pp. 719–724, 2008.
[7]	Turkoglu, D., Abuloha, M., and Abdeljawad, T., “KKM mappings in cone metric spaces and some fixed point theorems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 1, pp. 348–353, 2010.
[8]	[8]Sahin I., Telci, M., “Fixed points of contractive mappings on complete cone metric spaces,” Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 1, pp. 59–67, 2009.
[9]	Suzuki, T., “Fixed point theorems and convergence theorems for some generalized nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 340, no. 2, pp. 1088–1095, 2008. Fixed Point Theory and Applications 9.
[10]	Deimling, K., Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
[11]	Abdeljawad T., Karapinar, E., “Quasicone Metric Spaces and Generalizations of Caristi Kirk’s Theorem,” Fixed Point Theory and Applications, vol. 2009, p. 9 page, 2009.
[12]	Nieto, J. J., Rodrigez-Lopez, R., “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations” ActaMathematicaSinica, vol.23, no.12, pp.2205-2212, 2007.

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Elvin Rada, Agron Tato. (2015). An Extension of a Fixed Point Result in Cone Banach Space. Pure and Applied Mathematics Journal, 4(3), 70-74. https://doi.org/10.11648/j.pamj.20150403.12

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ACS Style

Elvin Rada; Agron Tato. An Extension of a Fixed Point Result in Cone Banach Space. Pure Appl. Math. J. 2015, 4(3), 70-74. doi: 10.11648/j.pamj.20150403.12

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Elvin Rada, Agron Tato. An Extension of a Fixed Point Result in Cone Banach Space. Pure Appl Math J. 2015;4(3):70-74. doi: 10.11648/j.pamj.20150403.12

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@article{10.11648/j.pamj.20150403.12,
  author = {Elvin Rada and Agron Tato},
  title = {An Extension of a Fixed Point Result in Cone Banach Space},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {3},
  pages = {70-74},
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  abstract = {In this paper we study a class of mappings in a ConeBanach Space which have at least one fixed point. More precisely for a closed and convex subset C of a cone Banach space with a generalized norm that satisfy a special condition. We are proposing some extensions of the results of Karapinar.},
 year = {2015}
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TY  - JOUR
T1  - An Extension of a Fixed Point Result in Cone Banach Space
AU  - Elvin Rada
AU  - Agron Tato
Y1  - 2015/04/24
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.12
DO  - 10.11648/j.pamj.20150403.12
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AB  - In this paper we study a class of mappings in a ConeBanach Space which have at least one fixed point. More precisely for a closed and convex subset C of a cone Banach space with a generalized norm that satisfy a special condition. We are proposing some extensions of the results of Karapinar.
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Author Information

Elvin Rada

Department of Mathematics, Facultyof Natural Sciences, University of Elbasan, Elbasan, Albania
Agron Tato

Department of Mathematics, Polytechnic University of Tirana, Tirana, Albania

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APA Style

Elvin Rada, Agron Tato. (2015). An Extension of a Fixed Point Result in Cone Banach Space. Pure and Applied Mathematics Journal, 4(3), 70-74. https://doi.org/10.11648/j.pamj.20150403.12

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ACS Style

Elvin Rada; Agron Tato. An Extension of a Fixed Point Result in Cone Banach Space. Pure Appl. Math. J. 2015, 4(3), 70-74. doi: 10.11648/j.pamj.20150403.12

Copy | Download

AMA Style

Elvin Rada, Agron Tato. An Extension of a Fixed Point Result in Cone Banach Space. Pure Appl Math J. 2015;4(3):70-74. doi: 10.11648/j.pamj.20150403.12

Copy | Download

@article{10.11648/j.pamj.20150403.12,
  author = {Elvin Rada and Agron Tato},
  title = {An Extension of a Fixed Point Result in Cone Banach Space},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {3},
  pages = {70-74},
  doi = {10.11648/j.pamj.20150403.12},
  url = {https://doi.org/10.11648/j.pamj.20150403.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150403.12},
  abstract = {In this paper we study a class of mappings in a ConeBanach Space which have at least one fixed point. More precisely for a closed and convex subset C of a cone Banach space with a generalized norm that satisfy a special condition. We are proposing some extensions of the results of Karapinar.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - An Extension of a Fixed Point Result in Cone Banach Space
AU  - Elvin Rada
AU  - Agron Tato
Y1  - 2015/04/24
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.12
DO  - 10.11648/j.pamj.20150403.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 70
EP  - 74
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.12
AB  - In this paper we study a class of mappings in a ConeBanach Space which have at least one fixed point. More precisely for a closed and convex subset C of a cone Banach space with a generalized norm that satisfy a special condition. We are proposing some extensions of the results of Karapinar.
VL  - 4
IS  - 3
ER  -

Copy | Download