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Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces. (English) Zbl 1197.54013
Summary: We give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.
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##### MSC:
 54A40 Fuzzy topology 54H25 Fixed-point and coincidence theorems (topological aspects)
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##### References:
 [1] Badard, R., Fixed point theorems for fuzzy numbers, Fuzzy set syst, 13, 291-302, (1984) · Zbl 0551.54005 [2] Bose, B.K.; Sabani, D., Fuzzy mappings and fixed point theorems, Fuzzy set syst, 21, 53-58, (1987) · Zbl 0609.54032 [3] Butnarin, D., Fixed point for fuzzy mappings, Fuzzy set syst, 7, 191-207, (1982) [4] Chang, S.S., Fixed point theorems for fuzzy mappings, Fuzzy set syst, 17, 181-187, (1985) · Zbl 0579.54034 [5] Chang, S.S.; Cho, Y.J.; Lee, B.S.; Jung, J.S.; Kang, S.M., Coincidence point and minimization theorems in fuzzy metric spaces, Fuzzy set syst, 88, 119-128, (1997) · Zbl 0912.54013 [6] Chang, S.S.; Cho, Y.J.; Lee, B.E.; Lee, G.M., Fixed degree and fixed point theorems for fuzzy mappings, Fuzzy set syst, 87, 325-334, (1997) · Zbl 0922.54016 [7] Cho, Y.J., Fixed points in fuzzy metric spaces, J fuzzy math, 5, 949-962, (1997) · Zbl 0887.54003 [8] Cho, Y.J.; Pathak, H.K.; Kang, S.M.; Jung, J.S., Common fixed points of compatible maps of type (β) on fuzzy metric spaces, Fuzzy set syst, 93, 99-111, (1998) · Zbl 0915.54004 [9] Deng, Z.K., Fuzzy psendo-metric spaces, J math anal appl, 86, 74-95, (1982) [10] Ereeg, M.A., Metric spaces in fuzzy set theory, J math anal appl, 69, 338-353, (1979) [11] El Naschie, M.S., On the uncertainty of Cantorian geometry and two-slit experiment, Chaos, solitons & fractals, 9, 517-529, (1998) · Zbl 0935.81009 [12] El Naschie, M.S., A review of E-infinity theory and the mass spectrum of high energy particle physics, Chaos, solitons & fractals, 19, 209-236, (2004) · Zbl 1071.81501 [13] El Naschie, M.S., On a fuzzy kahler-like manifold which is consistent with two-slit experiment, Int J nonlin sci numer simul, 6, 95-98, (2005) [14] El Naschie, M.S., The idealized quantum two-slit gedanken experiment revisited-criticism and reinterpretation, Chaos, solitons & fractals, 27, 9-13, (2006) · Zbl 1089.81500 [15] Fang, J.X., On fixed point theorems in fuzzy metric spaces, Fuzzy set syst, 46, 107-113, (1992) · Zbl 0766.54045 [16] George, A.; Veeramani, P., On some result in fuzzy metric space, Fuzzy set syst, 64, 395-399, (1994) · Zbl 0843.54014 [17] Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy set syst, 27, 385-389, (1988) · Zbl 0664.54032 [18] Gregori, V.; Sapena, A., On fixed-point theorem in fuzzy metric spaces, Fuzzy set syst, 125, 245-252, (2002) · Zbl 0995.54046 [19] Hadzic, O., Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces, Fuzzy set syst, 29, 115-125, (1989) · Zbl 0681.54023 [20] Jung, J.S.; Cho, Y.J.; Chang, S.S.; Kang, S.M., Coincidence theorems for set-valued mappings and ekland’s variational principle in fuzzy metric spaces, Fuzzy set syst, 79, 239-250, (1996) · Zbl 0867.54018 [21] Jungck, G., Commuting maps and fixed points, Amer math monthly, 83, 261-263, (1976) · Zbl 0321.54025 [22] Jungck, G., Compatible mappings and common fixed points, Int J math math sci, 9, 771-779, (1986) · Zbl 0613.54029 [23] Jungek, G.; Murthy, P.P.; Cho, Y.J., Compatible mappings of type (A) and common fixed points, Math jpn, 38, 381-390, (1993) · Zbl 0791.54059 [24] Kaleva, O.; Seikkala, S., On fuzzy metric spaces, Fuzzy set syst, 12, 215-229, (1984) · Zbl 0558.54003 [25] Kramosil, I.; Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetica, 11, 326-334, (1975) [26] Mishra, S.N.; Sharma, S.N.; Singh, S.L., Common fixed points of maps in fuzzy metric spaces, Int J math math sci, 17, 253-258, (1994) · Zbl 0798.54014 [27] Pathak, H.K.; Cho, Y.J.; Kang, S.M.; Lee, B.S., Fixed point theorems for compatible mappings of type (P) and applications to dynamic programming, Le matematische, L, 15-33, (1995) · Zbl 0877.54038 [28] Pathak, H.K.; Cho, Y.J.; Chang, S.S.; Kang, S.M., Compatible mappings of type (P) and fixed point theorems in metric spaces and probabilistic metric spaces, Novi sad J math, 26, 87-109, (1996) · Zbl 1030.47508 [29] Pathak, H.K.; Mishra, N.; Kalinde, A.K., Common fixed point theorems with applications to nonlinear integral equation, Demonstratio math, 32, 517-564, (1999) · Zbl 0939.47050 [30] Sessa, S., On some weak commutativity condition of mappings in fixed point considerations, Publ inst math (beograd), 32, 149-153, (1982) · Zbl 0523.54030 [31] Sharma, S.; Desphaude, B., Common fixed points of compatible maps of type(β) on fuzzy metric spaces, Demonsratio math, 35, 165-174, (2002) · Zbl 1055.54020 [32] Rodríguez López, J.; Ramaguera, S., The Hausdorff fuzzy metric on compact sets, Fuzzy set syst, 147, 273-283, (2004) · Zbl 1069.54009 [33] Miheţ, D., A Banach contraction theorem in fuzzy metric spaces, Fuzzy set syst, 144, 431-439, (2004) · Zbl 1052.54010 [34] Turkoglu D, Altun I, Cho YJ. Compatible maps and compatible maps of types (α) and (β) in intuitionistic fuzzy metric spaces, in press. [35] Schweizer, B.; Sherwood, H.; Tardiff, R.M., Contractions on PM-space examples and counterexamples, Stochastica, 1, 5-17, (1988) · Zbl 0689.60019 [36] Singh, B.; Jain, S., A fixed point theorem in Menger space through weak compatibility, J math anal appl, 301, 439-448, (2005) · Zbl 1068.54044 [37] Saadati, R.; Sedghi, S., A common fixed point theorem for R-weakly commutiting maps in fuzzy metric spaces, 6th Iranian conference on fuzzy systems, 387-391, (2006) [38] Sedghi, S.; Turkoglu, D.; Shobe, N., Generalization common fixed point theorem in complete fuzzy metric spaces, J. comput. anal. applictat, 9, 3, 337-348, (2007) · Zbl 1129.54028 [39] Tanaka, Y.; Mizno, Y.; Kado, T., Chaotic dynamics in Friedmann equation, Chaos, solitons & fractals, 24, 407-422, (2005) · Zbl 1070.83535 [40] Zadeh, L.A., Fuzzy sets, Inform control, 8, 338-353, (1965) · Zbl 0139.24606
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