Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces. (English) Zbl 1469.54058
Summary: We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give a unique fixed point result for a mapping satisfying a weak cyclical contractive condition. We also provide some illustrative examples.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
Keywords:
coincidence point; common fixed point; compatible mappings; cyclic weak \((\psi, \varphi)\)-contraction; partial metric space; weakly increasing mappingsReferences:
| [1] | Abbas M, Nazir T, Radenović S: Common fixed points of four maps in partially ordered metric spaces.Appl. Math. Lett. 2011, 24:1520-1526. · Zbl 1220.54018 · doi:10.1016/j.aml.2011.03.038 |
| [2] | Abbas, M, Sintunavarat, W, Kumam, P: Coupled fixed point in partially ordered G-metric spaces. Fixed Point Theory Appl. (to appear)Abbas, M, Sintunavarat, W, Kumam, P: Coupled fixed point in partially ordered G-metric spaces. Fixed Point Theory Appl. (to appear) · Zbl 1469.54028 |
| [3] | Agarwal RP, El-Gebeily MA, O’Regan D: Generalized contractions in partially ordered metric spaces.Appl. Anal. 2008, 87:109-116. · Zbl 1140.47042 · doi:10.1080/00036810701556151 |
| [4] | Altun, I.; Simsek, H., Some fixed point theorems on ordered metric spaces and application, No. 2010 (2010) · Zbl 1197.54053 |
| [5] | Altun, I.; Erduran, A., Fixed point theorems for monotone mappings on partial metric spaces, No. 2011 (2011) · Zbl 1207.54051 |
| [6] | Altun I, Sola F, Simsek H: Generalized contractions on partial metric spaces.Topol. Appl. 2010,157(18):2778-2785. · Zbl 1207.54052 · doi:10.1016/j.topol.2010.08.017 |
| [7] | Aydi H: Coincidence and common fixed point results for contraction type maps in partially ordered metric spaces.Int. J. Math. Anal. 2011,5(3):631-642. · Zbl 1238.54019 |
| [8] | Aydi H, Nashine HK, Samet B, Yazidi H: Coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations.Nonlinear Anal. 2011,74(17):6814-6825. · Zbl 1226.54043 · doi:10.1016/j.na.2011.07.006 |
| [9] | Aydi, H., Some coupled fixed point results on partial metric spaces, No. 2011 (2011) · Zbl 1213.54060 |
| [10] | Aydi H: Some fixed point results in ordered partial metric.J. Nonlinear Sci. Appl. 2011,4(3):210-217. · Zbl 1489.54068 |
| [11] | Aydi H: Fixed point results for weakly contractive mappings in ordered partial metric spaces.J. Adv. Math. Stud. 2011,4(2):1-12. · Zbl 1234.54051 |
| [12] | Aydi H: Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces.J. Nonlinear Analysis Optim. 2011,2(2):33-48. |
| [13] | Aydi H:Common fixed point results for mappings satisfying[InlineEquation not available: see fulltext.]-weak contractions in ordered partial metric spaces.Int. J. Math. Stat. 2012,12(2):53-64. · Zbl 1306.54041 |
| [14] | Aydi, H: A common fixed point result by altering distances involving a contractive condition of integral type in partial metric spaces. Demonstr. Math. 46(1/2) (2013) (in press)Aydi, H: A common fixed point result by altering distances involving a contractive condition of integral type in partial metric spaces. Demonstr. Math. 46(1/2) (2013) (in press) · Zbl 1291.54049 |
| [15] | Aydi H, Karapınar E, Shatanawi W:Coupled fixed point results for[InlineEquation not available: see fulltext.]-weakly contractive condition in ordered partial metric spaces.Comput. Math. Appl. 2011, 62:4449-4460. · Zbl 1236.54035 · doi:10.1016/j.camwa.2011.10.021 |
| [16] | Banach S: Sur les opérations dans les ensembles abstraits et leur application aux équations intgérales.Fundam. Math. 1922, 3:133-181. · JFM 48.0201.01 |
| [17] | Bhashkar TG, Lakshmikantham V: Fixed point theorems in partially ordered cone metric spaces and applications.Nonlinear Anal. 2006,65(7):825-832. |
| [18] | Ćirić, LB; Cakić, N.; Rajović, M.; Ume, JS, Monotone generalized nonlinear contractions in partially ordered metric spaces, No. 2008 (2008) · Zbl 1158.54019 |
| [19] | Ćirić LB, Samet B, Aydi H, Vetro C: Common fixed points of generalized contractions on partial metric spaces and an application.Appl. Math. Comput. 2011, 218:2398-2406. · Zbl 1244.54090 · doi:10.1016/j.amc.2011.07.005 |
| [20] | Di Bari C, Vetro P: Fixed points forφ-weak contractions on partial metric spaces.Int. J. Eng., Contemp. Math. Sci. 2011, 1:5-13. |
| [21] | Dukić, D.; Kadelburg, Z.; Radenović, S., Fixed points of Geraghty-type mappings in various generalized metric spaces, No. 2011 (2011) · Zbl 1231.54030 |
| [22] | Escardo MH: PCF extended with real numbers.Theor. Comput. Sci. 1996, 162:79-115. · Zbl 0871.68034 · doi:10.1016/0304-3975(95)00250-2 |
| [23] | Gopal, D.; Imdad, M.; Vetro, C.; Hasan, M., Fixed point theory for cyclic weak ϕ-contraction in fuzzy metric spaces, No. 2011 (2011) · Zbl 1214.54034 |
| [24] | Harjani J, Sadarangani K: Fixed point theorems for weakly contractive mappings in partially ordered sets.Nonlinear Anal. 2009, 71:3403-3410. · Zbl 1221.54058 · doi:10.1016/j.na.2009.01.240 |
| [25] | Jungck G: Compatible mappings and common fixed points.Int. J. Math. Math. Sci. 1986, 9:771-779. · Zbl 0613.54029 · doi:10.1155/S0161171286000935 |
| [26] | Karapinar E: Fixed point theory for cyclic weakϕ-contraction.Appl. Math. Lett. 2011, 24:822-825. · Zbl 1256.54073 · doi:10.1016/j.aml.2010.12.016 |
| [27] | Kirk WA, Srinivasan PS, Veeramani P: Fixed points for mappings satisfying cyclical contractive conditions.Fixed Point Theory 2003, 4:79-89. · Zbl 1052.54032 |
| [28] | Lakshmikantham V, Ćirić L: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces.Nonlinear Anal. 2009, 70:4341-4349. · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020 |
| [29] | Matthews, SG, Partial metric topology, 183-197 (1994) · Zbl 0911.54025 |
| [30] | Nashine HK, Samet B:Fixed point results for mappings satisfying[InlineEquation not available: see fulltext.]-weakly contractive condition in partially ordered metric spaces.Nonlinear Anal. 2011, 74:2201-2209. · Zbl 1208.41014 · doi:10.1016/j.na.2010.11.024 |
| [31] | Nieto JJ, Rodríguez-López R: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations.Order 2005, 22:223-239. · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5 |
| [32] | Nieto JJ, López RR: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations.Acta Math. Sin. Engl. Ser. 2007,23(12):2205-2212. · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0 |
| [33] | Oltra S, Valero O: Banach’s fixed point theorem for partial metric spaces.Rend. Ist. Mat. Univ. Trieste 2004,36(1-2):17-26. · Zbl 1080.54030 |
| [34] | O’Regan D, Petrusel A: Fixed point theorems for generalized contractions in ordered metric spaces.J. Math. Anal. Appl. 2008, 341:1241-1252. · Zbl 1142.47033 · doi:10.1016/j.jmaa.2007.11.026 |
| [35] | Pacurar M, Rus IA: Fixed point theory forϕ-contractions.Nonlinear Anal. 2010, 72:1181-1187. · Zbl 1191.54042 · doi:10.1016/j.na.2009.08.002 |
| [36] | Paesano D, Vetro P: Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces.Topol. Appl. 2012, 159:911-920. · Zbl 1241.54035 · doi:10.1016/j.topol.2011.12.008 |
| [37] | Radenović, S, Kadelburg, Z, Jandrlić, D, Jandrlić, A: Some results on weak contraction maps. Bull. Iranian Math. Soc. (to appear)Radenović, S, Kadelburg, Z, Jandrlić, D, Jandrlić, A: Some results on weak contraction maps. Bull. Iranian Math. Soc. (to appear) · Zbl 1391.54036 |
| [38] | Ran ACM, Reurings MCB: A fixed point theorem in partially ordered sets and some applications to matrix equations.Proc. Am. Math. Soc. 2004, 132:1435-1443. · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4 |
| [39] | Samet B: Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces.Nonlinear Anal. 2010, 72:4508-4517. · Zbl 1264.54068 · doi:10.1016/j.na.2010.02.026 |
| [40] | Samet, B.; Rajović, M.; Lazović, R.; Stoiljković, R., Common fixed point results for nonlinear contractions in ordered partial metric spaces, No. 2011 (2011) · Zbl 1271.54086 |
| [41] | Sintunavarat W, Cho YJ, Kumam P: Common fixed point theorems forc-distance in ordered cone metric spaces.Comput. Math. Appl. 2011, 62:1969-1978. · Zbl 1231.54028 · doi:10.1016/j.camwa.2011.06.040 |
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