FG-Coupled Fixed Point Theorems for Various Contractions in Partially Ordered Metric Spaces

Prajisha  E.; Shaini  P.

doi:10.5644/SJM.15.02.12

Authors

Prajisha E.
Shaini P.

DOI:

https://doi.org/10.5644/SJM.15.02.12

Keywords:

FG-coupled fixed point, Coupled fixed point, Mixed monotone property, Partially ordered set

Abstract

In this paper we introduce FG-coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FG-coupled fixed points for different contractive mappings. Our theorems generalizes the results of Gnana Bhaskar and Lakshmikantham [1].

Statistics

Abstract: 44 / PDF: 37

References

T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., Theory Methods Appl., 65 (2006) 1379 - 1393.

D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal., Theory Methods Appl., 11(5) (1987) 623-632.

J.J. Nieto and R. Rodriguez-Lopez, emph{Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005) 223 - 239.

J.J. Nieto and R.R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin., Engl. Ser., 23 (12) (2007) 2205 - 2212.

A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc., 132 (2003) 1435 - 1443.

F. Sabetghadam, H.P. Masiha and A.H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory Appl., 2009 (2009) 8.