Some Common Coupled Fixed Point Theorem for Two Pairs of w-compatible Maps in Complete Metric Space
Keywords:
Coupled fixed point, w-compatible maps, complete metric space
Abstract
The aim of this paper is to derive common coupled fixed point theorem for two pair of w-compatible self mappings under generalized rational contractive condition in metric spaces without considering completeness of whole space. Our result generalizes and improves related results existing in the literature. An example is given to support the usability of our results
References
T.G.Bhaskar and V.Lakshmikantham, Fixed point theorems in partial ordered metric spaces and applications, Nonlinear Anal., 65(2006) 1379-1393.
B.S.Choudhury, N.Meitya and P.Das, A coupled common fixed point theorem for a family of mappings, Nonlinear Anal., 18(1)(2013), 14-26.
B.K.Dass and S.Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math., 6(1975), 1455-1458.
D.Guo and V.Lakhsmikantham, Coupled fixed point of nonlinear operator with application, Nonlinear Anal., 11(1987), 623-632.
V.Lakshmikantham and Lj.B. Ciric, Coupled fixed point for nonlinear contraction in partially ordered metric spaces and application, Nonlinear Anal., 70(2009), 4341-4349.
H.K.Nashine, Z.Kadelburg and S.Radenovic, Coupled common fixed points theorems for w∗-compatible mappings in ordered cone metric spaces, Appl. Math. Comput., 218(2011), 5422-5432.
H.K.Nashine and W.Shatnawi, Coupled common fixed points theorems for pair of commuting mapping in partially ordered complete metric spaces, Comput. Math. Appl., 62(2011), 1984-1993.
H.K.Nashine and Z.Kadelburg, Partially ordered metric spaces, rational contractive expressions and coupled fixed points, Nonlinear Funct. Anal. Appl., 17(4)(2012), 471-489.
J.J.Nieto and R.R.Lopez, Contractive mappings theorems in partially ordered set and application to ordinary differential equations, Order, 22(2005), 223-239.
K.P.R.Rao, G.N.V.Kishore and N.V.Luong, A unique common coupled fixed point theorem for four maps under ψ-ϕ contractive condition in partial metric, Cubo a Mathematical Journal, 14(03)(2012), 115-127.
A.C.M.Ran and 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.
K.P.R.Rao and G.N.V.Kishore, A unique common fixed point theorem for four maps under ψ - φ contractive condition in partial metric spaces, Bulletin of Mathematical Anal. and Applications, 3(2011), 56-63.
B.S.Choudhury, N.Meitya and P.Das, A coupled common fixed point theorem for a family of mappings, Nonlinear Anal., 18(1)(2013), 14-26.
B.K.Dass and S.Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math., 6(1975), 1455-1458.
D.Guo and V.Lakhsmikantham, Coupled fixed point of nonlinear operator with application, Nonlinear Anal., 11(1987), 623-632.
V.Lakshmikantham and Lj.B. Ciric, Coupled fixed point for nonlinear contraction in partially ordered metric spaces and application, Nonlinear Anal., 70(2009), 4341-4349.
H.K.Nashine, Z.Kadelburg and S.Radenovic, Coupled common fixed points theorems for w∗-compatible mappings in ordered cone metric spaces, Appl. Math. Comput., 218(2011), 5422-5432.
H.K.Nashine and W.Shatnawi, Coupled common fixed points theorems for pair of commuting mapping in partially ordered complete metric spaces, Comput. Math. Appl., 62(2011), 1984-1993.
H.K.Nashine and Z.Kadelburg, Partially ordered metric spaces, rational contractive expressions and coupled fixed points, Nonlinear Funct. Anal. Appl., 17(4)(2012), 471-489.
J.J.Nieto and R.R.Lopez, Contractive mappings theorems in partially ordered set and application to ordinary differential equations, Order, 22(2005), 223-239.
K.P.R.Rao, G.N.V.Kishore and N.V.Luong, A unique common coupled fixed point theorem for four maps under ψ-ϕ contractive condition in partial metric, Cubo a Mathematical Journal, 14(03)(2012), 115-127.
A.C.M.Ran and 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.
K.P.R.Rao and G.N.V.Kishore, A unique common fixed point theorem for four maps under ψ - φ contractive condition in partial metric spaces, Bulletin of Mathematical Anal. and Applications, 3(2011), 56-63.
How to Cite
Hemant Kumar Nashine, & Anita Gupta. (2016). Some Common Coupled Fixed Point Theorem for Two Pairs of w-compatible Maps in Complete Metric Space. International Journal of Current Research in Science and Technology, 2(1), 41-50. Retrieved from https://crst.gfer.org/index.php/crst/article/view/58
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