×

Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces. (English) Zbl 1213.54012

Summary: We prove a common fixed point theorem for mappings under \(\phi\)-contractive conditions in fuzzy metric spaces. We also give an example to illustrate the theorem. The result is a genuine generalization of the corresponding result of S. Sedghi et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3-4, A, 1298–1304 (2010; Zbl 1180.54060)].

MSC:

54A40 Fuzzy topology
54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 1180.54060
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Zadeh LA: Fuzzy sets.Information and Computation 1965, 8: 338-353. · Zbl 0139.24606
[2] George A, Veeramani P: On some results in fuzzy metric spaces.Fuzzy Sets and Systems 1994,64(3):395-399. 10.1016/0165-0114(94)90162-7 · Zbl 0843.54014 · doi:10.1016/0165-0114(94)90162-7
[3] George A, Veeramani P: On some results of analysis for fuzzy metric spaces.Fuzzy Sets and Systems 1997,90(3):365-368. 10.1016/S0165-0114(96)00207-2 · Zbl 0917.54010 · doi:10.1016/S0165-0114(96)00207-2
[4] Bhaskar TG, Lakshmikantham V: Fixed point theorems in partially ordered metric spaces and applications.Nonlinear Analysis. Theory, Methods & Applications 2006,65(7):1379-1393. 10.1016/j.na.2005.10.017 · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
[5] Lakshmikantham V, Ćirić L: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces.Nonlinear Analysis. Theory, Methods & Applications 2009,70(12):4341-4349. 10.1016/j.na.2008.09.020 · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[6] Sedghi S, Altun I, Shobe N: Coupled fixed point theorems for contractions in fuzzy metric spaces.Nonlinear Analysis. Theory, Methods & Applications 2010,72(3-4):1298-1304. 10.1016/j.na.2009.08.018 · Zbl 1180.54060 · doi:10.1016/j.na.2009.08.018
[7] Fang J-X: Common fixed point theorems of compatible and weakly compatible maps in Menger spaces.Nonlinear Analysis. Theory, Methods & Applications 2009,71(5-6):1833-1843. 10.1016/j.na.2009.01.018 · Zbl 1172.54027 · doi:10.1016/j.na.2009.01.018
[8] Ćirić LB, Miheţ D, Saadati R: Monotone generalized contractions in partially ordered probabilistic metric spaces.Topology and its Applications 2009,156(17):2838-2844. 10.1016/j.topol.2009.08.029 · Zbl 1206.54039 · doi:10.1016/j.topol.2009.08.029
[9] O’Regan D, Saadati R: Nonlinear contraction theorems in probabilistic spaces.Applied Mathematics and Computation 2008,195(1):86-93. 10.1016/j.amc.2007.04.070 · Zbl 1135.54315 · doi:10.1016/j.amc.2007.04.070
[10] Jain S, Jain S, Bahadur Jain L: Compatibility of type (P) in modified intuitionistic fuzzy metric space.Journal of Nonlinear Science and its Applications 2010,3(2):96-109. · Zbl 1187.54039
[11] Ćirić LB, Ješić SN, Ume JS: The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces.Chaos, Solitons and Fractals 2008,37(3):781-791. 10.1016/j.chaos.2006.09.093 · Zbl 1137.54326 · doi:10.1016/j.chaos.2006.09.093
[12] \'Cirić L, Lakshmikantham V: Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces.Stochastic Analysis and Applications 2009,27(6):1246-1259. 10.1080/07362990903259967 · Zbl 1176.54030 · doi:10.1080/07362990903259967
[13] Ćirić, L.; Cakić, N.; Rajović, M.; Ume, JS, Monotone generalized nonlinear contractions in partially ordered metric spaces (2008) · Zbl 1158.54019
[14] Aliouche A, Merghadi F, Djoudi A: A related fixed point theorem in two fuzzy metric spaces.Journal of Nonlinear Science and its Applications 2009,2(1):19-24. · Zbl 1168.54017
[15] Ćirić L: Common fixed point theorems for a family of non-self mappings in convex metric spaces.Nonlinear Analysis. Theory, Methods & Applications 2009,71(5-6):1662-1669. 10.1016/j.na.2009.01.002 · Zbl 1203.54038 · doi:10.1016/j.na.2009.01.002
[16] Rao KPR, Aliouche A, Babu GR: Related fixed point theorems in fuzzy metric spaces.Journal of Nonlinear Science and its Applications 2008,1(3):194-202. · Zbl 1168.54023
[17] Ćirić L, Cakić N: On common fixed point theorems for non-self hybrid mappings in convex metric spaces.Applied Mathematics and Computation 2009,208(1):90-97. 10.1016/j.amc.2008.11.012 · Zbl 1163.47045 · doi:10.1016/j.amc.2008.11.012
[18] Ćirić L: Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces.Chaos, Solitons and Fractals 2009,42(1):146-154. 10.1016/j.chaos.2008.11.010 · Zbl 1198.54008 · doi:10.1016/j.chaos.2008.11.010
[19] Shakeri, S.; Ćirić, LJB; Saadati, R., Common fixed point theorem in partially ordered [InlineEquation not available: see fulltext.]-fuzzy metric spaces (2010)
[20] Ćirić L, Samet B, Vetro C: Common fixed point theorems for families of occasionally weakly compatible mappings.Mathematical and Computer Modelling 2011,53(5-6):631-636. 10.1016/j.mcm.2010.09.015 · Zbl 1217.54042 · doi:10.1016/j.mcm.2010.09.015
[21] Ćirić L, Abbas M, Saadati R, Hussain N: Common fixed points of almost generalized contractive mappings in ordered metric spaces.Applied Mathematics and Computation 2011,217(12):5784-5789. 10.1016/j.amc.2010.12.060 · Zbl 1206.54040 · doi:10.1016/j.amc.2010.12.060
[22] Ćirić L, Abbas M, Damjanović B, Saadati R: Common fuzzy fixed point theorems in ordered metric spaces.Mathematical and Computer Modelling 2011,53(9-10):1737-1741. 10.1016/j.mcm.2010.12.050 · Zbl 1219.54043 · doi:10.1016/j.mcm.2010.12.050
[23] Kamran T, Cakić N: Hybrid tangential property and coincidence point theorems.Fixed Point Theory 2008,9(2):487-496. · Zbl 1179.47045
[24] Hadžić O, Pap E: Fixed Point Theory in Probabilistic Metric Spaces, Mathematics and its Applications. Volume 536. Kluwer Academic, Dordrecht, The Netherlands; 2001:x+273.
[25] Grabiec M: Fixed points in fuzzy metric spaces.Fuzzy Sets and Systems 1988,27(3):385-389. 10.1016/0165-0114(88)90064-4 · Zbl 0664.54032 · doi:10.1016/0165-0114(88)90064-4
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.