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Some new fixed point theorems for a mixed monotone maps in partially ordered metric spaces. (English) Zbl 1295.54096

Summary: In this paper, we prove some new fixed point theorems for a mixed monotone mapping under more generalized nonlinear contractive conditions in a metric space endowed with partial order. Our results generalize and improve several results of T. Gnana Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 7, 1379–1393 (2006; Zbl 1106.47047)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
65J15 Numerical solutions to equations with nonlinear operators

Citations:

Zbl 1106.47047
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References:

[1] Guo DJ, Lakshmikantham V: Coupled fixed points of nonlinear operators with applications.Nonlinear Anal 1987, 11:623-632. · Zbl 0635.47045 · doi:10.1016/0362-546X(87)90077-0
[2] Guo DJ, Lakshmikantham V: Nonlinear problems in abstract cones. New York: Academic Press; 1988. · Zbl 0661.47045
[3] Zhang Z: New fixed point theorems of mixed monotone operators and applications.J. Math. Anal. Appl 1996, 204:307-319. · Zbl 0880.47036 · doi:10.1006/jmaa.1996.0442
[4] Guo DJ: Existence and uniqueness of positive fixed point for mixed monotone operators with applications.Appl. Anal 1992, 46:91-100. · Zbl 0792.47053 · doi:10.1080/00036819208840113
[5] Zhang SS, Ma YH: Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solution for a class of functional equations arising in dynamic programing.J. Math. Anal. Appl 1991, 160:468-479. · Zbl 0751.30016 · doi:10.1016/0022-247X(91)90330-3
[6] Guo DJ: Partial order methods in nonlinear analysis. Jinan: Shandong Science and Technology Press; 2000. (in Chinese)
[7] Song G: Iterative solutions for systems of nonlinear operator equations in Banach space.Acta Mathematica Scientia 2003, 23B:461-466. · Zbl 1047.47049
[8] Song G, Sun X, Zhao Y, Wang G: New common fixed point theorems for maps on cone metric spaces.Appl. Math. Lett 2010, 23:1033-1037. · Zbl 1195.54089 · doi:10.1016/j.aml.2010.04.032
[9] Samet B: Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces.Nonlinear Anal 2010, 72:4508-4517. · Zbl 1264.54068 · doi:10.1016/j.na.2010.02.026
[10] 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 Anal 2010, 72:2238-2242. · Zbl 1197.54054 · doi:10.1016/j.na.2009.10.023
[11] Luong N, Thuan N: Coupled fixed points in partially ordered metric spaces and application.Nonlinear Anal 2011, 74:983-992. · Zbl 1202.54036 · doi:10.1016/j.na.2010.09.055
[12] Abbas M, Khan A, Nazir T: Coupled common fixed point results in two generalized metric spaces.Appl. Math. Comput 2011, 217:6328-6336. · Zbl 1210.54048 · doi:10.1016/j.amc.2011.01.006
[13] Harjani J, López B, Sadarangani K: Fixed point theorems for mixed monotone operators and applications to integral equations.Nonlinear Anal 2011, 74:1749-1760. · Zbl 1218.54040 · doi:10.1016/j.na.2010.10.047
[14] Nashine H, Samet B, Vetro C: Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces.Math. Comput. Model 2011, 54:712-720. · Zbl 1225.54022 · doi:10.1016/j.mcm.2011.03.014
[15] Gnana Bhaskar T, Lakshmikantham V: Fixed point theorems in partially ordered metric spaces and applications.Nonlinear Anal 2006, 65:1379-1393. · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
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