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Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces. (English) Zbl 1225.54022
Summary: The purpose of this paper is to present some fixed point theorems for \(T\)-weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47H10 Fixed-point theorems
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[1] Khan, M.S.; Swaleh, M.; Sessa, S., Fixed point theorems by altering distances between the points, Bulletin of the Australian mathematical society, 30, 1, 1-9, (1984) · Zbl 0553.54023
[2] Agarwal, R.P.; El-Gebeily, M.A.; O’Regan, D., Generalized contractions in partially ordered metric spaces, Applicable analysis, 87, 1, 109-116, (2008) · Zbl 1140.47042
[3] Altun, I.; Durmaz, G., Some fixed point theorems on ordered cone metric spaces, Rendiconti del circolo matematico di Palermo, 58, 319-325, (2009) · Zbl 1184.54038
[4] Altun, I.; Simsek, H., Some fixed point theorems on ordered metric spaces and application, Fixed point theory and applications, (2010), Article ID 621492, 17 pages · Zbl 1197.54053
[5] Amini-Harandi, A.; Emami, H., A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear analysis, 72, 5, 2238-2242, (2010) · Zbl 1197.54054
[6] Beg, I.; Butt, A.R., Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear analysis, 71, 9, 3699-3704, (2009) · Zbl 1176.54028
[7] Beg, I.; Butt, A.R., Fixed points for weakly compatible mappings satisfying an implicit relation in partially ordered metric spaces, Carpathian journal of mathematics, 25, 1, 1-12, (2009) · Zbl 1199.54207
[8] Bhaskar, T.G.; Lakshmikantham, V., Fixed point theorems in partially ordered metric spaces and applications, Nonlinear analysis, 65, 7, 1379-1393, (2006) · Zbl 1106.47047
[9] Ćirić, L.; Cakić, N.; Rajović, M.; Ume, J.S., Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed point theory and applications, (2008), Article ID 131294, 11 pages · Zbl 1158.54019
[10] Nieto, J.J.; Rodríguez-López, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 3, 223-239, (2005) · Zbl 1095.47013
[11] Nieto, J.J.; Rodríguez-López, R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Mathematica sinica (English series), 23, 12, 2205-2212, (2007) · Zbl 1140.47045
[12] Nieto, J.J.; Pouso, R.L.; Rodríguez-López, R., Fixed point theorems in ordered abstract spaces, Proceedings of the American mathematical society, 135, 8, 2505-2517, (2007) · Zbl 1126.47045
[13] O’Regan, D.; Petrusel, A., Fixed point theorems for generalized contractions in ordered metric spaces, Journal of mathematical analysis and applications, 341, 2, 1241-1252, (2008) · Zbl 1142.47033
[14] Ran, A.C.M.; Reurings, M.C.B., A fixed point theorem in partially ordered sets and some applications to matrix equations, Proceedings of the American mathematical society, 132, 5, 1435-1443, (2004) · Zbl 1060.47056
[15] Harjani, J.; Sadarangani, K., Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear analysis, 71, 7-8, 3403-3410, (2009) · Zbl 1221.54058
[16] Harjani, J.; Sadarangani, K., Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear analysis, 72, 3-4, 1188-1197, (2010) · Zbl 1220.54025
[17] Jachymski, J., Equivalent conditions for generalized contractions on (ordered) metric spaces, Nonlinear analysis, 74, 768-774, (2011) · Zbl 1201.54034
[18] Vetro, C., Common fixed points in ordered Banach spaces, Le matematiche, 63, 2, 93-100, (2008) · Zbl 1228.47056
[19] Dhage, B.C., Condensing mappings and applications to existence theorems for common solution of differential equations, Bulletin of the Korean mathematical society, 36, 3, 565-578, (1999) · Zbl 0940.47043
[20] Dhage, B.C.; O’Regan, D.; Agrawal, R.P., Common fixed point theorems for a pair of countably condensing mappings in ordered Banach spaces, Journal of applied mathematics and stochastic analysis, 16, 3, 243-248, (2003) · Zbl 1068.47071
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