Cabrera, I.; Harjani, J.; Sadarangani, K. A fixed point theorem for contractions of rational type in partially ordered metric spaces. (English) Zbl 1319.54014 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 59, No. 2, 251-258 (2013). Summary: The purpose of this paper is to present a fixed point theorem due to B. K. Dass and S. Gupta [Indian J. Pure Appl. Math. 6, 1455–1458 (1975; Zbl 0371.54074)] in the context of partially ordered metric spaces. Cited in 2 ReviewsCited in 15 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 54E40 Special maps on metric spaces 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces Keywords:fixed point; partially ordered set Citations:Zbl 0371.54074 PDFBibTeX XMLCite \textit{I. Cabrera} et al., Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 59, No. 2, 251--258 (2013; Zbl 1319.54014) Full Text: DOI References: [1] Dass, B.K., Gupta, S.: An extension of Banach contraction principle through rational expressions. Inidan J. Pure Appl. Math. 6, 1455-1458 (1975) · Zbl 0371.54074 [2] Agarwal, R.P., El-Gebeily, M.A., O’Regan, D.: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87, 109-116 (2008) · Zbl 1140.47042 [3] 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. 72(5), 2238-2242 (2010) · Zbl 1197.54054 [4] Berinde, V.: Coupled fixed point theorems for \[\phi \]-contractive mixed monotone mappings in partially ordered metric spaces. Nonlinear Anal. 75(6), 3218-3228 (2012) · Zbl 1250.54043 [5] Choudhury, B.S., Kundu, A.: \[(\psi -\alpha -\beta )\]-weak contractions in partially ordered metric spaces. Appl. Math. Lett. 25(1), 6-10 (2012) · Zbl 1269.54021 [6] Gnana Bhaskar, T., Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65(7), 1379-1393 (2006) · Zbl 1106.47047 [7] Harjani, J., Sadarangani, K.: Fixed point theorems for mappings satisfying a condition of integral type in partially ordered sets. J. Conv. Anal. 17(2), 597-609 (2010) · Zbl 1192.54018 [8] Harjani, J., López, B., Sadarangani, K.: Fixed point theorems for weakly \[{\cal C}\]-contractive mappings in ordered metric spaces. Comput. Math. Appl. 61, 790-796 (2011) · Zbl 1217.54046 [9] Nieto, J.J., Rodríguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22(3), 223-239 (2005) · Zbl 1095.47013 [10] Nieto, J.J., Rodríguez-López, R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sinica 23(12), 2205-2212 (2007) · Zbl 1140.47045 [11] O’Regan, D., Petrusel, A.: Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl. 341(2), 1241-1252 (2008) · Zbl 1142.47033 [12] Rezapour, Sh, Amiri, P.: Fixed point of multivalued operators on ordered generalized metric spaces. Fixed Point Theory 13(1), 173-178 (2012) · Zbl 1329.54053 [13] Samet, B.: Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces. Nonlinear Anal. 72(12), 4508-4517 (2010) · Zbl 1264.54068 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.