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Coupled fixed points in partially ordered metric spaces and application. (English) Zbl 1202.54036
Summary: We prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces. The main results of this paper are generalizations of the main results of T. G. Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl. 65, No. 7 (A), 1379–1393 (2006; Zbl 1106.47047)]. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
45G10 Other nonlinear integral equations
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[1] Ran, A.C.M.; Reurings, M.C.B., A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. amer. math. soc., 132, 1435-1443, (2004) · Zbl 1060.47056
[2] Gnana Bhaskar, T.; Lakshmikantham, V., Fixed point theorems in partially ordered metric spaces and applications, Nonlinear anal. TMA, 65, 1379-1393, (2006) · Zbl 1106.47047
[3] Nieto, J.J.; Rodriguez-Lopez, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation, Order, 22, 223-239, (2005) · Zbl 1095.47013
[4] Nieto, J.J.; Rodriguez-Lopez, R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta math. sin. (engl. ser.), 23, 12, 2205-2212, (2007) · Zbl 1140.47045
[5] Agarwal, R.P.; El-Gebeily, M.A.; O’Regan, D., Generalized contractions in partially ordered metric spaces, Appl. anal., 87, 1-8, (2008) · Zbl 1140.47042
[6] Lakshmikantham, V.; Ćirić, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear anal. TMA, 70, 4341-4349, (2009) · Zbl 1176.54032
[7] Samet, B., Coupled fixed point theorems for a generalized meir – keeler contraction in partially ordered metric spaces, Nonlinear anal. TMA, (2010) · Zbl 1264.54068
[8] Altun, I.; Simsek, H., Some fixed point theorems on ordered metric spaces and application, Fixed point theory appl., 2010, (2010), 17 pages. Article ID 621469 · Zbl 1197.54053
[9] Harjani, J.; Sadarangani, K., Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear anal. TMA, 72, 1188-1197, (2010) · Zbl 1220.54025
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