Coupled fixed point theorems for nonlinear contractions in cone metric spaces. (Couple fixed point theorems for nonlinear contractions in cone metric spaces.) (English) Zbl 1198.65097

Summary: The notion of coupled fixed point is introduced by T. G. Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl. 65, No. 7 (A), 1379–1393 (2006; Zbl 1106.47047)]. In this manuscript, some results of V. Lakshmikantham and {Lj. Ćirić} [Nonlinear Anal., Theory Methods Appl. 70, No. 12 (A), 4341–4349 (2009; Zbl 1176.54032)] are extended to the class of cone metric spaces.


65J15 Numerical solutions to equations with nonlinear operators
47H10 Fixed-point theorems
Full Text: DOI


[1] Rzepecki, B., On fixed point theorems of maia type, Publ. inst. math., 28, 179-186, (1980) · Zbl 0482.47029
[2] Lin, Shy-Der, A common fixed point theroem in abstract spaces, Indian J. pure appl. math., 18, 8, 685-690, (1987) · Zbl 0622.47057
[3] Khan, M.S.; Imdad, M.A., A common fixed point theorem for a class of mappings, Indian J. pure appl. math., 14, 1220-1227, (1983) · Zbl 0533.54031
[4] Huang, Long-Guang; Zhang, Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. math. anal. appl., 332, 1468-1476, (2007) · Zbl 1118.54022
[5] Lakshmikantham, V.; Ćirić, L., Couple fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear anal., 70, 4341-4349, (2009) · Zbl 1176.54032
[6] Rezapour, Sh.; Hamlbarani, R., Some notes on the paper “cone metric spaces and fixed point theorems of contractive mappings”, J. math. anal. appl., 347, 719-724, (2008) · Zbl 1145.54045
[7] Abdeljawad, T., Completion of cone metric spaces, Hacet. J. math. stat., 39, 1, 67-74, (2010) · Zbl 1195.54057
[8] Abdeljawad, T.; Karapınar, E., Quasicone metric spaces and generalizations of Caristi kirk’s theorem, Fixed point theory appl., (2009) · Zbl 1197.54051
[9] Turkoglu, D.; Abuloha, M., Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta math. sin. (engl. ser.), 26, 3, 489-496, (2010) · Zbl 1203.54049
[10] Turkoglu, D.; Abuloha, M.; Abdeljawad, T., KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear anal. TMA, 72, 1, 348-353, (2010) · Zbl 1197.54076
[11] Di Bari, C.; Vetro, P., \(\phi\)-pairs and common fixed points in cone metric spaces, Rend. circ. mat. Palermo (2), 57, 2, 279-285, (2008) · Zbl 1164.54031
[12] Karapınar, E., Fixed point theorems in cone Banach spaces, Fixed point theory appl., 2009, (2009), 9 pages doi:10.1155/2009/609281. Article ID 609281 · Zbl 1204.47066
[13] Bhaskar, T.G.; Lakshmikantham, V., Fixed point theory in partially ordered metric spaces and applications, Nonlinear anal., 65, 1379-1393, (2006) · Zbl 1106.47047
[14] E. Karapınar, Couple fixed point on cone metric spaces, Gazi University J. Sci. (in press). · Zbl 1198.65097
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