Coupled Fixed Point Theorem in Partially Ordered Metric Spaces

Virendra Singh Chouhan^1, and Richa Sharma^2,

¹Department of Mathematics, Lovely Professional University, Jalandhar, India

²Department of Applied Sciences, Rayat Bahra Institute of Engineering & Nano-Technology, Hoshiarpur, India

Cite this paper:
Virendra Singh Chouhan and Richa Sharma. Coupled Fixed Point Theorem in Partially Ordered Metric Spaces. American Journal of Mathematical Analysis. 2014; 2(2):19-22. doi: 10.12691/ajma-2-2-1

Abstract

In this paper, we obtain some unique coupled fixed point theorem in a complete metric space endowed with a partial order. We also give example to validate the main result in this paper.

Keywords:
Coupled fixed point partial ordered complete metric space

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References:

[1]	H. Alaeidizaji, V. Parvaneh, Coupled fixed point results in complete partial metric space, lnternational. Journal of mathematical sciences, Artical ID 670410 (2012).
[2]	H. Aydi, Some coupled fixed point results on partial metric spaces, lnternational Journal of Mathematical Sciences, Artical ID 647091 (2011).
[3]	T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: Theory, Methods and Apllications, 65(7) (2006), 1379-1393.
[4]	L.Ciric, V. Lakshmikantham, Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stochastic and Applications 27, (2009), 1246-1259.
[5]	L.Ciric, V. Lakshmikantham, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods and Applications 70 (12), (2009), 4341-4349.
[6]	L.Ciric, M.O. Olatinwo, D. Gopal, G. Akinbo, Coupled fixed point theorems for mappings satisfing a contractions of rational type on a partially ordered metric space, Advances in Fixed Point Theory, 2 No. 1, (2012), 1-8.
[7]	S.G. Matthews, Partial metric topology, in: Proc 8th summer conference on general topology and application, in Annals of the New York Academy of Sciences, Vol.728, pp. (1994), 183-197.
[8]	S. J. O'Neill, Two topologies are better than one, Tech. Rep., University of warwick, Coventry, UK (1995).
[9]	S. J. O'Neil,l Partial metrics, valuations and domain theory, in: Proc 11th summer conference on general topology and application, in Annals of the New York Academy of Sciences, Vol.806, (1996), 304-315.
[10]	F. Sabetghadam, H.P. Masiha, A.H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory and Applications, Article ID 125426 (2009).
[11]	W.Zhong, X. Yang, F. Gao, A cauchy problem for some local fractional abstract differential equation with fractal conditions, J. Applied Functional Analysis, Vol.8, No. 1(2013), 92-99.