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Fixed point theorems for weakly contractive mappings in partially ordered sets. (English) Zbl 1221.54058
Summary: The purpose of this paper is to present some fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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[1] Alber, Ya.I.; Guerre-Delabriere, S., Principles of weakly contractive maps in Hilbert spaces, new results in operator theory, (), 7-22 · Zbl 0897.47044
[2] Rhoades, B.E., Some theorems on weakly contractive maps, Nonlinear anal., 47, 2683-2693, (2001) · Zbl 1042.47521
[3] Agarwal, R.P.; El-Gebeily, M.A.; O’Regan, D., Generalized contractions in partially ordered metric spaces, Appl. anal., 87, 109-116, (2008) · Zbl 1140.47042
[4] Dz. Burgic, S. Kalabusic, M.R.S. Kulenovic, Global attractivity results for mixed monotone mappings in partially ordered complete metric spaces, Fixed Point Theory and Applications (in press) · Zbl 1168.54327
[5] L. Ciric, N. Cakid, M. Rajovic, J.S. Uma, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory and Applications (in press)
[6] Gnana Bhaskar, T.; Lakshmikantham, V., Fixed points theorem in partially ordered metric spaces and applications, Nonlinear anal., 65, 1379-1393, (2006) · Zbl 1106.47047
[7] V. Lakshmikantham, L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., in press (doi:10.1016/j.na.2008.09.020) · Zbl 1176.54030
[8] Nieto, J.J.; Rodríguez-López, R., Existence of extremal solutions for quadratic fuzzy equations, Fixed point theory and applications, 2005, 321-342, (2005) · Zbl 1102.54004
[9] Nieto, J.J.; Rodríguez-López, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013
[10] Nieto, J.J.; Rodríguez-López, R., Applications of contractive-like mapping principles to fuzzy equations, Rev. mat. complut., 19, 361-383, (2006) · Zbl 1113.26030
[11] Nieto, J.J.; Pouso, R.L.; Rodríguez-López, R., Fixed point theorems in ordered abstract spaces, Proc. amer. math. soc., 135, 2505-2517, (2007) · Zbl 1126.47045
[12] Nieto, J.J.; Rodríguez-López, R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta math. sinica, 23, 2205-2212, (2007) · Zbl 1140.47045
[13] O’Regan, D.; Petrusel, A., Fixed point theorems for generalized contractions in ordered metric spaces, J. math. anal. appl., 341, 2, 1241-1252, (2008) · Zbl 1142.47033
[14] Petrusel, A.; Rus, I.A., Fixed point theorems in ordered L-spaces, Proc. amer. math. soc., 134, 411-418, (2006) · Zbl 1086.47026
[15] 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
[16] Wu, Y., New fixed point theorems and applications of mixed monotone operator, J. math. anal. appl., 341, 883-893, (2008) · Zbl 1137.47044
[17] Aliouche, A., Common fixed point theorems of Gregus type for weakly compatible mappings satisfying generalized contractive conditions, J. math. anal. appl., 341, 707-719, (2008) · Zbl 1138.54031
[18] Altun, I.; Turkoglu, D.; Rhoades, B.E., Fixed points of weakly compatible maps satisfying a general contractive condition of integral type, Fixed point theory and applications, (2007), Article ID 17301 · Zbl 1153.54022
[19] Cabada, A.; Nieto, J.J., Fixed points and approximate solutions for nonlinear operator equations, J. comput. appl. math., 113, 17-25, (2000) · Zbl 0954.47038
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