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A generalization of Mizoguchi and Takahashi’s theorem for single-valued mappings in partially ordered metric spaces. (English) Zbl 1220.54023
Summary: We present a generalization of Mizoguchi and Takahashi’s fixed point theorem for single-valued mappings in partially ordered metric spaces. As an application of the main result, we give an existence and uniqueness theorem for the solution of a periodic boundary value problem.

54H25Fixed-point and coincidence theorems in topological spaces
Full Text: DOI
[1] Jr., S. B. Nadler: Multi-valued contraction mappings, Pacific J. Math. 30, 475-488 (1969) · Zbl 0187.45002
[2] Turinici, M.: Abstract comparison principles and multivariable Gronwall--Bellman inequalities, J. math. Anal. appl. 117, 100-127 (1986) · Zbl 0613.47037 · doi:10.1016/0022-247X(86)90251-9
[3] Ran, A. C. M.; Reurings, M. C. B.: A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. amer. Math. soc. 132, 1435-1443 (2004) · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
[4] Nieto, J. J.; Lopez, R. R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22, 223-239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[5] O’regan, D.; Petrusel, A.: Fixed point theorems for generalized contractions in ordered metric spaces, J. math. Anal. appl. 341, 1241-1252 (2008) · Zbl 1142.47033 · doi:10.1016/j.jmaa.2007.11.026
[6] Bhaskar, T. G.; Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications, Nonlinear anal. 65, 1379-1393 (2006) · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
[7] Lakshmikantham, V.; Ćirić, Lj.B.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear anal. 70, 4341-4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[8] Samet, B.: Coupled fixed point theorems for a generalized Meir--Keeler contraction in partially ordered metric spaces, Nonlinear anal. 72, 4508-4517 (2010) · Zbl 1264.54068
[9] Amini-Harandi, A.; O’regan, D.: Fixed point theorems for set-valued contraction type maps in metric spaces, J. fixed point theory appl., 1-7 (2010) · Zbl 1188.54014 · doi:10.1155/2010/390183
[10] Reich, S.: Fixed points of contractive functions, Boll. unione mat. Ital. (4) 5, 26-42 (1972) · Zbl 0249.54026
[11] Mizoguchi, N.; Takahashi, W.: Fixed point theorems for multivalued mappings on complete metric space, J. math. Anal. appl. 141, 177-188 (1989) · Zbl 0688.54028 · doi:10.1016/0022-247X(89)90214-X
[12] Du, W. -S.: Coupled fixed point theorems for nonlinear contractions satisfied mizoguchi--takahashi’s condition in quasiordered metric spaces, Fixed point theory appl. 2010 (2010) · Zbl 1194.54061 · doi:10.1155/2010/876372