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Coupled coincidence points for two mappings in metric spaces and cone metric spaces. (English) Zbl 1414.54021

Summary: This article is concerned with coupled coincidence points and common fixed points for two mappings in metric spaces and cone metric spaces. We first establish a coupled coincidence point theorem for two mappings and a common fixed point theorem for two \(w\)-compatible mappings in metric spaces. Then, by using a scalarization method, we extend our main theorems to cone metric spaces. Our results generalize and complement several earlier results in the literature. Especially, our main results complement a very recent result due to M. Abbas et al. [Appl. Math. Comput. 217, No. 1, 195–202 (2010; Zbl 1197.54049)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces

Citations:

Zbl 1197.54049
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References:

[1] Abbas M, Ali Khan M, Radenović S: Common coupled fixed point theorems in cone metric spaces for w-compatible mappings.Appl Math Comput 2010, 217:195-202. · Zbl 1197.54049 · doi:10.1016/j.amc.2010.05.042
[2] Gnana Bhaskar T, Lakshmikantham V: Fixed point theorems in partially ordered metric spaces and applications.Nonlinear Anal 2006, 65:1379-1393. · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
[3] Sabetghadam F, Masiha HP, Sanatpour AH: Some coupled fixed point theorems in cone metric space.Fixed Point Theory Appl 2009, 2009:8. (Article ID 125426) · Zbl 1179.54069 · doi:10.1155/2009/125426
[4] 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
[5] Karapinar E: Couple fixed point theorems for nonlinear contractions in cone metric spaces.Comput Math Appl 2010, 59:3656-3668. · Zbl 1198.65097 · doi:10.1016/j.camwa.2010.03.062
[6] Mitrović ZD: A coupled best approximations theorem in normed spaces.Nonlinear Anal 2010, 72:4049-4052. · Zbl 1185.47059 · doi:10.1016/j.na.2010.01.035
[7] Ding HS, Li L, Radojević S: Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces.Fixed Point Theory Appl 2012, 2012:96. · Zbl 1420.54071 · doi:10.1186/1687-1812-2012-96
[8] Du WS: A note on cone metric fixed point theory and its equivalence.Nonlinear Anal 2010, 72:2259-2261. · Zbl 1205.54040 · doi:10.1016/j.na.2009.10.026
[9] Huang LG, Zhang X: Cone metric spaces and fixed point theorems of contractive mappings.J Math Anal Appl 2007, 332:1468-1476. · Zbl 1118.54022 · doi:10.1016/j.jmaa.2005.03.087
[10] Abbas M, Jungck G: Common fixed point results of noncommuting mappings without continuity in cone metric spaces.J Math Anal Appl 2008, 341:418-420. · Zbl 1147.54022 · doi:10.1016/j.jmaa.2007.09.070
[11] Altun I, Durmaz G: Some fixed point results in cone metric spaces.Rendiconti del Circolo Mathematico di Palermo 2009, 58:319-325. · Zbl 1184.54038 · doi:10.1007/s12215-009-0026-y
[12] Altun I, Damjanović B, Djorić D: Fixed point and common fixed point theorems on ordered cone metric spaces.Appl Math Lett 2010, 23:310-316. · Zbl 1197.54052 · doi:10.1016/j.aml.2009.09.016
[13] Ding HS, Li L: Coupled fixed point theorems in partially ordered cone metric spaces.Filomat 2011, 25:137-149. · Zbl 1289.54122 · doi:10.2298/FIL1102137D
[14] Ding HS, Li L, Long W: Coupled common fixed point theorems for weakly increasing mappings with two variables.J Comput Anal Appl to appear · Zbl 1284.54055
[15] Dorić, D.; Kadelburg, Z.; Radenović, S., Coupled fixed point for mappings without mixed monotone property (2012) · Zbl 1295.54097
[16] Golubović Z, Kadelburg Z, Radenović S: Coupled coincidence points of mappings in ordered partial metric spaces.Abstr Appl Anal 2012, 2012:18. (Article ID 192581) · Zbl 1241.54033
[17] Ilić D, Rakočević V: Common fixed points for maps on cone metric space.J Math Anal Appl 2008, 341:876-882. · Zbl 1156.54023 · doi:10.1016/j.jmaa.2007.10.065
[18] Ilić D, Rakočević V: Quasi-contraction on a cone metric space.Appl Math Lett 2009, 22:728-731. · Zbl 1179.54060 · doi:10.1016/j.aml.2008.08.011
[19] Janković S, Kadelburg Z, Radenović S: Rhoades BE: Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces.Fixed Point Theory Appl 2009, 2009:16. (Article ID 761086) · Zbl 1186.54035
[20] Jungck G, Radenović S, Radojević S, Rakočević V: Common fixed point theorems for weakly compatible pairs on cone metric spaces.Fixed Point Theory Appl 2009, 2009:13. (Article ID 643840) · Zbl 1190.54032 · doi:10.1155/2009/643840
[21] Kadelburg Z, Radenović S, Rakočvić V: Remarks on quasi-contraction on a cone metric space.Appl Math Lett 2009, 22:1674-1679. · Zbl 1180.54056 · doi:10.1016/j.aml.2009.06.003
[22] Kadelburg Z, Pavlović M, Radenović S: Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces.Comput Math Appl 2010, 59:3148-3159. · Zbl 1193.54035 · doi:10.1016/j.camwa.2010.02.039
[23] Kadelburg Z, Radenović S, Rakočević V: A note on the equivalence of some metric and cone metric fixed point results.Appl Math Lett 2011, 24:370-374. · Zbl 1213.54067 · doi:10.1016/j.aml.2010.10.030
[24] Kadelburg, Z.; Radenović, S., Coupled fixed point results under tvs-cone metric and w-cone-distance (2012)
[25] Nashine HK, Kadelburg Z, Radenović S: Coupled common fixed point theorems for w*-compatible mappings in ordered cone metric spaces.Appl Math Comput 2012, 218:5422-5432. · Zbl 1267.54050 · doi:10.1016/j.amc.2011.11.029
[26] Radenović S, Rhoades BE: Fixed point theorem for two non-self mappings in cone metric spaces.Comput Math Appl 2009, 57:1701-1707. · Zbl 1186.65073 · doi:10.1016/j.camwa.2009.03.058
[27] Rezapour Sh, Hamlbarani R: Some note on the paper “Cone metric spaces and fixed point theorems of contractive mappings”.J Math Anal Appl 2008, 345:719-724. · Zbl 1145.54045 · doi:10.1016/j.jmaa.2008.04.049
[28] Rezapour Sh, Haghi RH, Shahzad N: Some notes on fixed points of quasi-contraction maps.Appl Math Lett 2010, 23:498-502. · Zbl 1206.54061 · doi:10.1016/j.aml.2010.01.003
[29] Zhang, X., Fixed point theorem of generalized quasicontractive mapping in cone metric spaces (2011)
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