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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.

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
[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 · doi:10.1016/j.na.2005.10.017
[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 · doi:10.1016/j.na.2010.06.025
[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)
[4]Lakshmikantham V., L.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. TMA 70, 4341–4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[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 · doi:10.1016/j.na.2010.02.026
[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)
[7]Rhoades B.E.: Some theorems on weakly contractive maps. Nonlinear Anal. TMA 47(4), 2683–2693 (2001) · Zbl 1042.47521 · doi:10.1016/S0362-546X(01)00388-1
[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(1), 189–199 (2002) · Zbl 1005.47053 · doi:10.1016/S0022-247X(02)00063-X
[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 · doi:10.1016/j.na.2009.08.040
[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 · doi:10.1016/j.na.2010.11.017
[11]Dorić D.: Common fixed point for generalized (ψ, ϕ)-weak contractions. Appl. Math. Lett. 22, 1896–1900 (2009) · Zbl 1203.54040 · doi:10.1016/j.aml.2009.08.001
[12]Zhang Q., Song Y.: Fixed point theory for generalized $${phi}$$ -weak contractions. Appl. Math. Lett. 22(1), 75–78 (2009) · Zbl 1163.47304 · doi:10.1016/j.aml.2008.02.007
[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 · doi:10.1017/S0004972700001659
[14]Choudhury B.S.: A common unique fixed point result in metric spaces involving generalised altering distances. Math. Commun. 10, 105–110 (2005)
[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 · doi:10.1016/j.chaos.2009.04.020
[16]Miheţ D.: Altering distances in probabilistic Menger spaces. Nonlinear Anal. TMA 71, 2734–2738 (2009) · Zbl 1176.54034 · doi:10.1016/j.na.2009.01.107
[17]Naidu S.V.R.: Some fixed point theorems in Metric spaces by altering distances. Czechoslov. Math. J. 53(1), 205–212 (2003) · Zbl 1013.54011 · doi:10.1023/A:1022991929004
[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(6), 641–647 (1999)
[19]Dutta, P.N., Choudhury, B.S.: A generalisation of contraction principle in metric spaces. Fixed Point Theory Appl. 2008, Article ID 406368 (2008)
[20]Jungck G.: Commuting mappings and fixed points. Am. Math. Mon. 83, 261–263 (1976) · Zbl 0321.54025 · doi:10.2307/2318216
[21]Jungck G.: Compatible mappings and common fixed points. Int. J. Math. Math. Sci. 9, 771–779 (1986) · Zbl 0613.54029 · doi:10.1155/S0161171286000935
[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)
[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)
[24]Berinde V.: A common fixed point theorem for compatible quasi contractive self mappings in metric spaces. Appl. Math. Comput. 213(2), 348–354 (2009) · Zbl 1203.54036 · doi:10.1016/j.amc.2009.03.027
[25]Kang S.M., Cho Y.J., Jungck G.: Common fixed point of compatible mappings. Int. J. Math. Math. Sci. 13(1), 61–66 (1990) · Zbl 0711.54029 · doi:10.1155/S0161171290000096