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A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space. (English) Zbl 1203.54041

Summary: The purpose of this paper is to present a fixed point theorem using a contractive condition of rational type in the context of partially ordered metric spaces.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
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References:

[1] D. S. Jaggi, “Some unique fixed point theorems,” Indian Journal of Pure and Applied Mathematics, vol. 8, no. 2, pp. 223-230, 1977. · Zbl 0379.54015
[2] R. P. Agarwal, M. A. El-Gebeily, and D. O’Regan, “Generalized contractions in partially ordered metric spaces,” Applicable Analysis, vol. 87, no. 1, pp. 109-116, 2008. · Zbl 1140.47042
[3] T. Gnana Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 7, pp. 1379-1393, 2006. · Zbl 1106.47047
[4] J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 3403-3410, 2009. · Zbl 1221.54058
[5] J. Harjani and K. Sadarangani, “Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1188-1197, 2010. · Zbl 1220.54025
[6] V. Lakshmikantham and L. Ciric, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 12, pp. 4341-4349, 2009. · Zbl 1176.54030
[7] J. J. Nieto and R. Rodríguez-López, “Existence of extremal solutions for quadratic fuzzy equations,” Fixed Point Theory and Applications, vol. 2005, no. 3, pp. 321-342, 2005. · Zbl 1102.54004
[8] J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223-239, 2005. · Zbl 1095.47013
[9] J. J. Nieto and R. Rodríguez-López, “Applications of contractive-like mapping principles to fuzzy equations,” Revista Matemática Complutense, vol. 19, no. 2, pp. 361-383, 2006. · Zbl 1113.26030
[10] J. J. Nieto, R. L. Pouso, and R. Rodríguez-López, “Fixed point theorems in ordered abstract spaces,” Proceedings of the American Mathematical Society, vol. 135, no. 8, pp. 2505-2517, 2007. · Zbl 1126.47045
[11] J. J. Nieto and R. Rodríguez-López, “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations,” Acta Mathematica Sinica, vol. 23, no. 12, pp. 2205-2212, 2007. · Zbl 1140.47045
[12] D. O’Regan and A. Petru\csel, “Fixed point theorems for generalized contractions in ordered metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 1241-1252, 2008. · Zbl 1142.47033
[13] A. Petru\csel and I. A. Rus, “Fixed point theorems in ordered L-spaces,” Proceedings of the American Mathematical Society, vol. 134, no. 2, pp. 411-418, 2006. · Zbl 1086.47026
[14] A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 1435-1443, 2004. · Zbl 1060.47056
[15] Y. Wu, “New fixed point theorems and applications of mixed monotone operator,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 883-893, 2008. · Zbl 1137.47044
[16] A. Cabada and J. J. Nieto, “Fixed points and approximate solutions for nonlinear operator equations,” Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 17-25, 2000. · Zbl 0954.47038
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