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Coupled coincidence point theorems in ordered metric spaces. (English) Zbl 1253.54037
The authors provide a generalization for the contraction fixed point principle that states the existence of the so-called coupled coincidences of a pair of maps defined on an ordered complete metric space. Neither convincing examples of possible concrete applications nor arguments justifying the importance of the problem are given.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems
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##### References:
 [1] Gnana Bhaskar, T.; Lakshmikantham, V., Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA, 65, 1379-1393, (2006) · Zbl 1106.47047 [2] Choudhury, B.S.; Kundu, A., A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. TMA, 73, 2524-2531, (2010) · Zbl 1229.54051 [3] Harjani, J.; Lopez, B.; Sadarangani, K., Fixed point theorems for mixed monotone operators and applications to integral equations, nonlinear anal, TMA, 74, 1749-1760, (2011) · Zbl 1218.54040 [4] Lakshmikantham, V.; Ćirić, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. TMA, 70, 4341-4349, (2009) · Zbl 1176.54032 [5] Samet, B., Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. TMA, 72, 4508-4517, (2010) · Zbl 1264.54068 [6] Alber, Ya. I., Guerre-Delabriere, S.: Principles of weakly contractive maps in Hilbert spaces. In: Gohberg, I., Lyubich, Yu. (eds.) New Results in Operator Theory. Advances and Appl., vol. 98, pp. 7-22. Birkhäuser, Basel (1997) · Zbl 0897.47044 [7] Rhoades, B.E., Some theorems on weakly contractive maps, Nonlinear Anal. TMA, 47, 2683-2693, (2001) · Zbl 1042.47521 [8] Chidume, C.E.; Zegeye, H.; Aneke, S.J., Approximation of fixed points of weakly contractive nonself maps in Banach spaces, J. Math. Anal. Appl., 270, 189-199, (2002) · Zbl 1005.47053 [9] Choudhury, B.S.; Metiya, N., Fixed points of weak contractions in cone metric spaces, Nonlinear Anal. TMA, 72, 1589-1593, (2010) · Zbl 1191.54036 [10] Choudhury, B.S.; Konar, P.; Rhoades, B.E.; Metiya, N., Fixed point theorems for generalized weakly contractive mappings, Nonlinear Anal. TMA, 74, 2116-2126, (2011) · Zbl 1218.54036 [11] Dorić, D., Common fixed point for generalized ($$ψ$$, $$φ$$)-weak contractions, Appl. Math. Lett., 22, 1896-1900, (2009) · Zbl 1203.54040 [12] Zhang, Q.; Song, Y., Fixed point theory for generalized $${ϕ}$$ -weak contractions, Appl. Math. Lett., 22, 75-78, (2009) · Zbl 1163.47304 [13] Khan, M.S.; Swaleh, M.; Sessa, S., Fixed points theorems by altering distances between the points, Bull. Aust. Math. Soc., 30, 1-9, (1984) · Zbl 0553.54023 [14] Choudhury, B.S., A common unique fixed point result in metric spaces involving generalised altering distances, Math. Commun., 10, 105-110, (2005) · Zbl 1089.54514 [15] Choudhury, B.S.; Das, K., A coincidence point result in Menger spaces using a control function, Chaos Solitons Fractals, 42, 3058-3063, (2009) · Zbl 1198.54072 [16] Miheţ, D., Altering distances in probabilistic Menger spaces, Nonlinear Anal. TMA, 71, 2734-2738, (2009) · Zbl 1176.54034 [17] Naidu, S.V.R., Some fixed point theorems in metric spaces by altering distances, Czechoslov. Math. J., 53, 205-212, (2003) · Zbl 1013.54011 [18] Sastry, K.P.R.; Babu, G.V.R., Some fixed point theorems by altering distances between the points, Ind. J. Pure. Appl. Math., 30, 641-647, (1999) · Zbl 0938.47044 [19] Dutta, P.N., Choudhury, B.S.: A generalisation of contraction principle in metric spaces. Fixed Point Theory Appl. 2008, Article ID 406368 (2008) · Zbl 1177.54024 [20] Jungck, G., Commuting mappings and fixed points, Am. Math. Mon., 83, 261-263, (1976) · Zbl 0321.54025 [21] Jungck, G., Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, 771-779, (1986) · Zbl 0613.54029 [22] Babu, G.V.R.; Vara Prasad, K.N.V.V., Common fixed point theorems of different compatible type mappings using ciric’s contraction type condition, Math. Commun., 11, 87-102, (2006) · Zbl 1120.47045 [23] Bari, C.D., Vetro, C.: Common fixed point theorems for weakly compatible maps satisfying a general contractive condition. Int. J. Math. Math. Sci. 2008, Article ID 891375 (2008) · Zbl 1151.54340 [24] Berinde, V., A common fixed point theorem for compatible quasi contractive self mappings in metric spaces, Appl. Math. Comput., 213, 348-354, (2009) · Zbl 1203.54036 [25] Kang, S.M.; Cho, Y.J.; Jungck, G., Common fixed point of compatible mappings, Int. J. Math. Math. Sci., 13, 61-66, (1990) · Zbl 0711.54029
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