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Coupled fixed point theorems in partially ordered metric spaces

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Języki publikacji
EN
Abstrakty
EN
This paper deals with some coupled fixed point theorems for a mapping with mixed monotone property and satisfying certain generalized rational contraction in a partially ordered metric space. Also, the result for the existence and uniqueness of a coupled fixed point to the map is given under ordered relation in a space. These results generalize and extend some existing results in the literature.
Rocznik
Tom
Strony
77--89
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
  • Department of Applied Mathematics School of Applied Natural Sciences Adama Science and Technology University, Post Box No. 1888, Adama, Ethiopia
autor
  • Department of Mathematics Vignan’s Foundation for Science Technology & Research Vadlamudi-522213, Andhra Pradesh, India
Bibliografia
  • [1] Edelstein M., On fixed points and periodic points under contraction mappings, J. Lond. Math. Soc., 37 (1962), 74-79.
  • [2] Hardy G.C., Rogers T., A generalization of fixed point theorem of S. Reich, Can. Math. Bull., 16(1973), 201-206.
  • [3] Kannan R., Some results on fixed points-II, Am. Math. Mon., 76(1969), 71-76.
  • [4] Reich S., Some remarks concerning contraction mappings, Can. Math. Bull., 14(1971), 121-124.
  • [5] Singh M.R., Chatterjee A.K., Fixed point theorems, Commun. Fac. Sci. Univ. Ank., Series A1 37(1988), 1-4.
  • [6] Smart D.R., Fixed Point Theorems, Cambridge University Press, Cambridge, 1974.
  • [7] Wong C.S., Common fixed points of two mappings, Pac. J. Math., 48(1973), 299-312.
  • [8] Wolk E.S., Continuous convergence in partially ordered sets, Gen. Topol. Appl., 5(1975), 221-234.
  • [9] Monjardet B., Metrics on partially ordered sets - a survey, Discrete Math., 35(1981), 173-184.
  • [10] Ran A.C.M., Reurings M.C.B., A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Am. Math. Soc., 132(2004), 1435-1443.
  • [11] Nieto J.J., Lopez R.R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22(2005), 223-239.
  • [12] Nieto J.J., Lopez R.R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equation, Acta Math. Sin. Engl. Ser., 23(12)(2007), 2205-2212.
  • [13] Nieto J.J., Pouso L., Rodríguez-López R., Fixed point theorems in ordered abstract spaces, Proc. Am. Math. Soc., 135(2007), 2505-2517.
  • [14] Hong S., Fixed points of multivalued operators in ordered metric spaces with applications, Nonlinear Anal., Theory Methods Appl., 72(2010), 3929-3942.
  • [15] Ozturk M., Basarir M., On some common fixed point theorems with rational expressions on cone metric spaces over a Banach algebra, Hacet. J. Math. Stat., 41(2)(2012), 211-222.
  • [16] Rouzkard F., Imdad M., Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl., (2012). DOI:10.1016/ j.camwa.2012.02.063.
  • [17] Ahmad J., Arshad M., Vetro C., On a theorem of Khan in a generalized metric space, Int. J. Anal. 2013, Article ID 852727, (2013).
  • [18] Altun I., Damjanovic B., Djoric D., Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett., 23(2010), 310-316.
  • [19] 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., Theory Methods Appl., 72(2010), 2238-2242.
  • [20] Arshad M., Azam A., Vetro P., Some common fixed results in cone metric spaces, Fixed Point Theory Appl. 2009, Article ID 493965 (2009).
  • [21] Arshad M., Ahmad J., Karapinar E., Some common fixed point results in rectangular metric spaces, Int. J. Anal. 2013, Article ID 307234 (2013).
  • [22] Azam A., Fisher B., Khan M., Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 32(3)(2011), 243-253.
  • [23] Zhang X., Fixed point theorems of multivalued monotone mappings in ordered metric spaces, Appl. Math. Lett., 23(2010), 235-240.
  • [24] Bhaskar T.G., Lakshmikantham V., Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal., Theory Methods Appl., 65(2006), 1379-1393.
  • [25] Lakshmikantham V., Cirić L.B., Couple fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., Theory Methods Appl., 70 (2009), 4341-4349.
  • [26] Cirić L., Damjanović B., Jleli M., Samet B., Coupled fixed point theorems for generalized Mizoguchi-Takahashi contractions with applications, Fixed Point Theory And Applications (2012), 2012, 2012:51. DOI:10.1186/1687-1812-2012-51.
  • [27] Aydi H., Karapinar E., Shatanawi W., Coupled fixed point results for (ψ, φ)-weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl., 62(12)(2011), 4449-4460.
  • [28] Chandok S., Narang T.D., Taoudi M.A., Some coupled fixed point theorems for mappings satisfying a generalized contractive condition of rational type, Palestine Journal of Mathematics, 4(2)(2015), 360-366.
  • [29] Choudhury B.S., Kundu A., A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., Theory Methods Appl., 73(2010), 2524-2531.
  • [30] Cirić L., Olatinwo M. O., Gopal D., Akinbo G., Coupled fixed point theorems for mappings satisfying a contractive condition of rational type on a partially ordered metric space, Advances in Fixed Point Theory, 2(1)(2012), 1-8.
  • [31] Karapinar E., Coupled fixed point on cone metric spaces, Gazi Univ. J. Sci., 24(1)(2011), 51-58.
  • [32] Kumam P., Rouzkard F., Imdad M., GopalD., Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction, Abstract and Applied Analysis, 2013, Article ID 206515, 9 pages. http://dx.doi.org/10.1155/2013/206515.
  • [33] Luong N.V., Thuan N.X., Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal., Theory Methods Appl., 74(2011), 983-992.
  • [34] Samet B., Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 74(12)(2010), 4508-4517.
  • [35] Zhou M., Liu Xiao I., Dolićanin Dekić D., Damjanović B., Coupled coincidence point results for Geraghty type contraction by using monotone property in partially ordered S metric spaces, Journal of Nonlinear Sciences and Applications, 9 br 12 (2016), 5950-5969.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bf6fc4a4-0fd7-4a58-9d67-c84c14aa7598
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