Jiang, Shujun; Li, Zhilong Generalized contractions of rational type in ordered partial metric spaces. (English) Zbl 1470.54068 Abstr. Appl. Anal. 2013, Article ID 928017, 7 p. (2013). Summary: Without the continuity and nondecreasing property of the comparison function, we in this paper prove some fixed point theorems of generalized contractions of rational type in ordered partial metric spaces, which generalize and improve the corresponding results of Luong and Thuan. An example is given to support the usability of our results. MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. PDF BibTeX XML Cite \textit{S. Jiang} and \textit{Z. Li}, Abstr. Appl. Anal. 2013, Article ID 928017, 7 p. (2013; Zbl 1470.54068) Full Text: DOI References: [1] Jaggi, D. S., Some unique fixed point theorems, Indian Journal of Pure and Applied Mathematics, 8, 2, 223-230 (1977) · Zbl 0379.54015 [2] Harjani, J.; López, B.; Sadarangani, K., A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space, Abstract and Applied Analysis, 2010 (2010) · Zbl 1203.54041 [3] Luong, N. V.; Thuan, N. X., Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces, Fixed Point Theory and Applications, 2011 (2011) · Zbl 1315.54040 [4] Matthews, S. G., Partial metric topology, Annals of the New York Academy of Sciences, 728, 183-197 (1994) · Zbl 0911.54025 [5] Oltra, S.; Valero, O., Banach’s fixed point theorem for partial metric spaces, Rendiconti dell’Istituto di Matematica dell’Università di Trieste, 36, 1-2, 17-26 (2004) · Zbl 1080.54030 [6] Altun, I.; Sola, F.; Simsek, H., Generalized contractions on partial metric spaces, Topology and Its Applications, 157, 18, 2778-2785 (2010) · Zbl 1207.54052 [7] Altun, I.; Sadarangani, K., Corrigendum to “Generalized contractions on partial metric spaces” [Topology Appl. 157 (2010) 2778-2785], Topology and Its Applications, 158, 13, 1738-1740 (2011) · Zbl 1226.54041 [8] Romaguera, S., Fixed point theorems for generalized contractions on partial metric spaces, Topology and Its Applications, 159, 1, 194-199 (2012) · Zbl 1232.54039 [9] Amini-Harandi, A., Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory and Applications, 2012 (2012) · Zbl 1398.54064 [10] Bukatin, M.; Kopperman, R.; Matthews, S.; Pajoohesh, H., Partial metric spaces, American Mathematical Monthly, 116, 8, 708-718 (2009) · Zbl 1229.54037 [11] Karapınar, E.; Erhan, I. M., Fixed point theorems for operators on partial metric spaces, Applied Mathematics Letters, 24, 11, 1894-1899 (2011) · Zbl 1229.54056 [12] Romaguera, S., A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and Applications, 2010 (2010) · Zbl 1193.54047 [13] Ilić, D.; Pavlović, V.; Rakočević, V., Some new extensions of Banach’s contraction principle to partial metric space, Applied Mathematics Letters, 24, 8, 1326-1330 (2011) · Zbl 1292.54025 [14] Ćirić, L.; Samet, B.; Aydi, H.; Vetro, C., Common fixed points of generalized contractions on partial metric spaces and an application, Applied Mathematics and Computation, 218, 6, 2398-2406 (2011) · Zbl 1244.54090 [15] Samet, B.; Rajović, M.; Lazović, R.; Stojiljković, R., Common fixed point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory and Applications, 2011 (2011) · Zbl 1271.54086 [16] Abdeljawad, T.; Karapınar, E.; Taş, K., Existence and uniqueness of a common fixed point on partial metric spaces, Applied Mathematics Letters, 24, 11, 1900-1904 (2011) · Zbl 1230.54032 [17] Bari, C. D.; Milojević, M.; Radenović, S.; Vetro, P., Common fixed points for self-mappings on partial metric spaces, Fixed Point Theory and Applications, 2012 (2012) · Zbl 1277.54031 [18] Alghamdi, M. A.; Shahzad, N.; Valero, O., On fixed point theory in partial metric spaces, Fixed Point Theory and Applications, 2012 (2012) · Zbl 1469.54044 [19] Erduran, A., Common fixed point of \(g\)-approximative multivalued mapping in ordered partial metric space, Fixed Point Theory and Applications, 2013 (2013) · Zbl 1282.05079 [20] Ilić, D.; Pavlović, V.; Rakočević, V., Extensions of the Zamfirescu theorem to partial metric spaces, Mathematical and Computer Modelling, 55, 3-4, 801-809 (2012) · Zbl 1255.54022 [21] Vetro, F.; Radenović, S., Nonlinear \(\psi \)-quasi-contractions of Ćirić-type in partial metric spaces, Applied Mathematics and Computation, 219, 4, 1594-1600 (2012) · Zbl 1291.54073 [22] Abdeljawad, T., Fixed points for generalized weakly contractive mappings in partial metric spaces, Mathematical and Computer Modelling, 54, 11-12, 2923-2927 (2011) · Zbl 1237.54038 [23] Haghi, R. H.; Rezapour, S.; Shahzad, N., Be careful on partial metric fixed point results, Topology and Its Applications, 160, 3, 450-454 (2013) · Zbl 1267.54044 [24] Berinde, V., A common fixed point theorem for compatible quasi contractive self mappings in metric spaces, Applied Mathematics and Computation, 213, 2, 348-354 (2009) · Zbl 1203.54036 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.