×

Common fixed point theorems for families of compatible mappings in intuitionistic fuzzy metric spaces. (English) Zbl 1205.54009

Summary: We prove some common fixed point theorems for any even number of compatible mappings in complete intuitionistic fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces and intuitionistic fuzzy metric spaces.

MSC:

54A40 Fuzzy topology
54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abu-Donia H.M., Nase A.A.: Common fixed point theorems in intuitionistic fuzzy metric spaces. Fuzzy Syst. Math. 22, 100-106 (2008) · Zbl 1332.54204
[2] Alaca C.: On fixed point theorems in intuitionistic fuzzy metric spaces. Commun. Korean Math. Soc. 24, 565-579 (2009) · Zbl 1231.54005 · doi:10.4134/CKMS.2009.24.4.565
[3] Alaca C., Altun I., Turkoglu D.: On Compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces. Commun. Korean Math. Soc. 23, 427-446 (2008) · Zbl 1168.54324 · doi:10.4134/CKMS.2008.23.3.427
[4] Alaca C., Turkoglu D., Yildiz C.: Fixed points in intuitionistic fuzzy metric spaces. Chaos Solit. Fract. 29, 1073-1078 (2006) · Zbl 1142.54362 · doi:10.1016/j.chaos.2005.08.066
[5] Atanassov, K.: Intuitionistic fuzzy sets. In: Sgurev, V. (ed.) VII ITKR’s Session, Sofia June, 1983. Central Science and Technology Library, Bulgrian Academy of Sciences (1984) · Zbl 1488.03039
[6] Atanassov K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87-96 (1986) · Zbl 0631.03040 · doi:10.1016/S0165-0114(86)80034-3
[7] Atanassov K.: New operators defined over the intuitionistic fuzzy sets. Fuzzy Sets Syst. 61, 137-142 (1994) · Zbl 0824.04004 · doi:10.1016/0165-0114(94)90229-1
[8] Ciric L.B., Jesic S.N., Ume J.S.: The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces. Chaos Solit. Fract. 32, 781-791 (2008) · Zbl 1137.54326 · doi:10.1016/j.chaos.2006.09.093
[9] Cho Y.J.: Fixed points in fuzzy metric spaces. J. Fuzzy Math. 5, 949-962 (1997) · Zbl 0887.54003
[10] Coker D.: An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst. 88, 81-89 (1997) · Zbl 0923.54004 · doi:10.1016/S0165-0114(96)00076-0
[11] Coker D., Demirsi M.: An introduction to intuitionistic fuzzy topological spaces in Sostak’s sense. Busefal 67, 67-76 (1996)
[12] Dubois D., Prade H.: Fuzzy sets: Theory and Applications to Policy Analysis and Information Systems. Plenum Press, New York (1980) · Zbl 0444.94049
[13] Fang J.X.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46, 107-113 (1992) · Zbl 0766.54045 · doi:10.1016/0165-0114(92)90271-5
[14] George A., Veeramani P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395-399 (1994) · Zbl 0843.54014 · doi:10.1016/0165-0114(94)90162-7
[15] Grabiec M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385-389 (1988) · Zbl 0664.54032 · doi:10.1016/0165-0114(88)90064-4
[16] Gregori V., Sapena A.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 125, 245-253 (2002) · Zbl 0995.54046 · doi:10.1016/S0165-0114(00)00088-9
[17] Gregori V., Ramaguera S.: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115, 485-489 (2000) · Zbl 0985.54007 · doi:10.1016/S0165-0114(98)00281-4
[18] Hadzic O., Pap E.: Fixed Point Theory in PM-spaces. Kluwer, Dordrecht (2001) · Zbl 0994.47077
[19] Huang X.J., Zhu C.X., Wen X.: Common fixed point theorems for families of maps in complete L-fuzzy metric spaces. Filomat 23, 67-80 (2009) · Zbl 1265.54171 · doi:10.2298/FIL0903067H
[20] Imdad M., Ali J., Tanveer M.: Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces. Chaos Solit. Fract. 42, 3121-3129 (2009) · Zbl 1198.54076 · doi:10.1016/j.chaos.2009.04.017
[21] Jungck G.: Compatible mappings and common fixed points. Int. J. Math. Math. Sci. 9, 771-779 (1986) · Zbl 0613.54029 · doi:10.1155/S0161171286000935
[22] Klement E.P.: Operations on fuzzy sets: an axiomatic approach. Inf. Sci. 27, 221-232 (1984) · Zbl 0515.03036 · doi:10.1016/0020-0255(82)90026-3
[23] Klement E.P., Mesiar R., Pap E.: A characterization of the ordering of continuous t-norms. Fuzzy Sets Syst. 86, 189-195 (1997) · Zbl 0914.04006 · doi:10.1016/0165-0114(95)00407-6
[24] Klement E.P., Mesiar R., Pap E.: Triangular Norms, Trends in Logic 8. Kluwer, Dordrecht (2000) · Zbl 0972.03002
[25] Kramosil I., Michalek J.: Fuzzy metric and statistical metric spaces. Kybernetica 11, 326-334 (1975)
[26] Lowen R.: Fuzzy Set Theory. Kluwer, Dordrecht (1996) · Zbl 0854.04006
[27] Menger K.: Statistical metrics. Proc. Natl. Acad. Sci. USA 28, 535-537 (1942) · Zbl 0063.03886 · doi:10.1073/pnas.28.12.535
[28] Mishra S.N., Sharma N., Singh S.L.: Common fixed points of maps on fuzzy metric spaces. Int. J. Math. Sci. 17, 253-258 (1994) · Zbl 0798.54014 · doi:10.1155/S0161171294000372
[29] Mohamad A.: Fixed-point theorems in intuitionistic fuzzy metric spaces. Chaos Solit. Fract. 34, 1689-1695 (2007) · Zbl 1152.54362 · doi:10.1016/j.chaos.2006.05.024
[30] Park J.H.: Intuitionistic fuzzy metric spaces. Chaos Solit. Fract. 22, 1039-1046 (2004) · Zbl 1060.54010 · doi:10.1016/j.chaos.2004.02.051
[31] Romaguera P., Tirado S.: Conraction maps on Ifqm-spaces with application with recurrence equations of quicksort. Electron. Notes Theor. Comput. Sci. 225, 269-279 (2009) · Zbl 1336.54050 · doi:10.1016/j.entcs.2008.12.080
[32] Saadati R., Vaezpour S.M., Cho Y.J.: Quicksort algorithm: application of fixed point theorem in intuitionistic fuzzy quasi Metric spaces at domain of words. J. Comput. Appl. Math. 228, 219-225 (2009) · Zbl 1189.68040 · doi:10.1016/j.cam.2008.09.013
[33] Samanta S.K., Mondal T.K.: Intuitionistic gradation of openness: intuitionistic fuzzy topology. Busefal 73, 8-17 (1997)
[34] Samanta S.K., Mondal T.K.: On intuitionistic gradation of openness. Fuzzy Sets Syst. 131, 323-336 (2002) · Zbl 1026.54002 · doi:10.1016/S0165-0114(01)00235-4
[35] Schweizer B., Sklar A.: Statistical metric spaces. Pac. J. Math. 10, 314-334 (1960) · Zbl 0091.29801
[36] Sessa S.: On a weak commutative condition in fixed point consideration. Publ. Inst. Math. (Beograd) 32, 146-153 (1982)
[37] Sharma S.: Common fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 127, 345-352 (2002) · Zbl 0990.54029 · doi:10.1016/S0165-0114(01)00112-9
[38] Sharma S., Deshpande B.: Common fixed point theorems for finite number of mappings without continuity and compatibilityon intuitionistic fuzzy metric spaces. Chaos Solit. Fract. 40, 2242-2256 (2009) · Zbl 1198.54089 · doi:10.1016/j.chaos.2007.10.011
[39] Turkoglu D., Alaca C., Yildiz C.: Compatible maps and compatible maps of types (α) and (β) in intuitionistic fuzzy metric spaces. Demonstr. Math. 39, 671-684 (2006) · Zbl 1112.54014
[40] Vasuki R.: A common fixed point theorem in a fuzzy metric space. Fuzzy Sets Syst. 97, 395-397 (1998) · Zbl 0926.54005 · doi:10.1016/S0165-0114(96)00342-9
[41] Zadeh L.A.: Fuzzy sets. Inf. Control 8, 338-353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
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.