Fixed point and common fixed point results in ordered cone metric spaces

Binayak S. Choudhury; N. Metiya

doi:10.2478/v10309-012-0005-8

.blurhash-client-img { display: none !important; }

Fixed point and common fixed point results in ordered cone metric spaces

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 20 (2012): Issue 1 (May 2012)

By: Binayak S. Choudhury and N. Metiya

Open Access

|May 2013

Abstract

In this paper we establish some fixed point results for functions which satisfy certain weak contractive inequalities in partially ordered cone metric spaces. We have also given some illustrative examples. Our results are extension of some existing

References

[1] R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Applicable Analysis 87 (2008), 109-116.10.1080/00036810701556151
Search in Google Scholar
[2] Ya. I. Alber, S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, in :I. Gohberg, Yu. Lyubich(Eds.), New Results in Operator Theory, in : Advances and Appl. 98, Birkhuser, Basel, 1997, 7-22.
Search in Google Scholar
[3] I. Altun, B. Damjanovic, D. Djoric, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett. 23 (2010), 310-316.10.1016/j.aml.2009.09.016
Search in Google Scholar
[4] C. E. Chidume, H. Zegeye, S. J. Aneke, Approximation of fixed points of weakly contractive nonself maps in Banach spaces, J. Math. Anal. Appl. 270(1) (2002), 189-199.10.1016/S0022-247X(02)00063-X
Search in Google Scholar
[5] B. S. Choudhury, A common unique fixed point result in metric spaces involving generalised altering distances, Math. Commun. 10 (2005), 105-110.
Search in Google Scholar
[6] B. S. Choudhury, P. N. Dutta, Common fixed points for fuzzy mappings using generalized altering distances, Soochow J. Math. 31(1) (2005), 71-81.
Search in Google Scholar
[7] B. S. Choudhury, K. Das, A coincidence point result in Menger spaces using a control function, Chaos Solitons and Fractals 42 (2009), 3058-3063.10.1016/j.chaos.2009.04.020
Search in Google Scholar
[8] B. S. Choudhury, P. N. Dutta, K. Das, A fixed points result in Menger space using a real function, Acta. Math. Hungar. 122 (2009), 203-216.10.1007/s10474-008-7242-3
Search in Google Scholar
[9] B. S. Choudhury, N. Metiya, Fixed points of weak contractions in cone metric spaces, Nonlinear Anal. 72 (2010), 1589-1593.10.1016/j.na.2009.08.040
Search in Google Scholar
[10] B. S. Choudhury, N. Metiya, The point of coincidence and common fixed point for a pair of mappings in cone metric spaces, Comput. Math. Appl. 60 (2010), 1686-1695.10.1016/j.camwa.2010.06.048
Search in Google Scholar
[11] K. Deimling, Nonlinear Functional Analysis, Springer-Verlage, 1985.10.1007/978-3-662-00547-7
Search in Google Scholar
[12] D. Dorić, Common fixed point for generalized (ψ, φ)-weak contractions, Appl. Math. Lett. 22 (2009), 1896-1900.10.1016/j.aml.2009.08.001
Search in Google Scholar
[13] P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl. 2008 (2008), Article ID 406368.
Search in Google Scholar
[14] R. H. Haghi, Sh. Rezapour, Fixed points of multifunctions on regular cone metric spaces, Expo. Math. 28 (2010), 71-77.10.1016/j.exmath.2009.04.001
Search in Google Scholar
[15] J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. 71 (2009), 3403-3410.10.1016/j.na.2009.01.240
Search in Google Scholar
[16] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468-1476.10.1016/j.jmaa.2005.03.087
Search in Google Scholar
[17] D. Ilić, V. Rakočević, Common fixed point for maps on cone metric space, J. Math. Anal. Appl. 341 (2008), 876-882.10.1016/j.jmaa.2007.10.065
Search in Google Scholar
[18] J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces, Nonlinear Anal. 74 (2011), 768-774.10.1016/j.na.2010.09.025
Search in Google Scholar
[19] S. Jankovi´c, Z. Kadelburg, S. Radenovi´c, B. E. Rhoades, Assad-Kirk- Type Fixed Point Theorems for a Pair of Nonself Mappings on Cone Metric Spaces, Fixed Point Theory Appl. Volume 2009 (2009), Article ID 761086, 16 pages.10.1155/2009/761086
Search in Google Scholar
[20] G. Jungck, S. Radenovi´c, S. Radojevi´c, V. Rakoˇcevi´c, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl. Volume 2009 (2009), Article ID 643840, 13 pages.10.1155/2009/643840
Search in Google Scholar
[21] M. S. Khan, M. Swaleh, S. Sessa, Fixed points theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), 1-9.10.1017/S0004972700001659
Search in Google Scholar
[22] S. V. R. Naidu, Some fixed point theorems in metric spaces by altering distances, Czechoslovak Math. Jr. 53(1) (2003), 205-212.10.1023/A:1022991929004
Search in Google Scholar
[23] J. J. Nieto, R. Rodrguez-Lpez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica 23 (2007), 2205-2212.10.1007/s10114-005-0769-0
Search in Google Scholar
[24] J. O. Olaleru, Some generalizations of fixed point theorems in cone metric spaces, Fixed Point Theory Appl. Volume 2009 (2009), Article ID 657914, 10 pp.10.1155/2009/657914
Search in Google Scholar
[25] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443. 10.1090/S0002-9939-03-07220-4
Search in Google Scholar
[26] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47(4) (200l), 2683-2693.10.1016/S0362-546X(01)00388-1
Search in Google Scholar
[27] K. P. R. Sastry, G. V. R. Babu, Some fixed point theorems by altering distances between the points, Ind. J. Pure. Appl. Math. 30(6) (1999), 641-647.
Search in Google Scholar
[28] M. Turinici, Abstract comparison principles and multivariable Gronwall- Bellman inequalities, J. Math. Anal. Appl. 117 (1986), 100-127.10.1016/0022-247X(86)90251-9
Search in Google Scholar
[29] Q. Zhang, Y. Song, Fixed point theory for generalized ɸ− weak contractions, Appl. Math. Lett. 22(1) (2009), 75-78. 10.1016/j.aml.2008.02.007
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10309-012-0005-8 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 55 - 72

Published on: May 17, 2013

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Partially ordered set,

Cone metric space,

Weak contractive inequality,

Related subjects:

© 2013 Binayak S. Choudhury, N. Metiya, published by Ovidius University of Constanta
This work is licensed under the Creative Commons License.

Volume 20 (2012): Issue 1 (May 2012)