×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.