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Common fixed points of fuzzy maps. (English) Zbl 1165.54311
Summary: We prove common fixed point theorems for a pair of fuzzy mappings satisfying Edelstein, Alber and Guerr-Delabriere type contractive conditions in a metric linear space.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54A40 Fuzzy topology 47H10 Fixed-point theorems 47S40 Fuzzy operator theory
##### Keywords:
fixed point; contractive type mappings; fuzzy set; fuzzy mapping
Full Text:
##### References:
 [1] Heilpern, S., Fuzzy mappings and fixed point theorems, J. math. anal. appl., 83, 566-569, (1981) · Zbl 0486.54006 [2] Bose, R.K.; Sahani, D., Fuzzy mappings and fixed point theorems, Fuzzy sets and systems, 21, 53-58, (1987) · Zbl 0609.54032 [3] Lee, B.S.; Cho, S.J., A fixed point theorem for contractive type fuzzy mappings, Fuzzy sets and systems, 61, 309-312, (1994) · Zbl 0831.54036 [4] Rashwan, R.A.; Ahmad, M.A., Common fixed point theorems for fuzzy mappings, Arch. math. (Brno), 38, 219-226, (2002) · Zbl 1068.54008 [5] Rhoades, B.E., A common fixed point theorem for sequence of fuzzy mappings, Int. J. math. math. sci., 8, 447-450, (1995) · Zbl 0840.47049 [6] Ko, H.M.; Tasi, Y.H., Fixed point theorems for localized property, Tamkang J. math., 8, 1, 81-85, (1977) [7] Reich, S., Fixed points of contractive functions, Boll. unione mat. ital., 4, 5, 24-26, (1972) · Zbl 0249.54026 [8] Nadler, S.B., Multivalued contraction mappings, Pacific J. math., 30, 475-488, (1969) · Zbl 0187.45002 [9] Hu, T., Fixed point theorems for multivalued mappings, Canad. math. bull., 23, 193-197, (1980) · Zbl 0436.54037 [10] Edelstein, M., An extension of banach’s contraction principle, Proc. amer. math. soc., 12, 7-12, (1961) · Zbl 0096.17101 [11] Bailey, D.F., Some theorems on contractive mappings, J. lond. math. soc., 41, 101-106, (1996) · Zbl 0132.18805 [12] Beg, I.; Azam, A., Fixed points of multivalued locally contractive mappings, Boll. unione mat. ital. (4A), 7, 227-233, (1990) · Zbl 0717.54023 [13] Holmes, R.D., On fixed and periodic points under certain set of mappings, Canad. math. bull., 12, 813-822, (1969) · Zbl 0198.27801 [14] Hu, T.; Rosen, H., Locally contractive and expansive mappings, Proc. amer. math. soc., 86, 656-662, (1982) · Zbl 0519.54030 [15] Waters, C., A fixed point theorem for locally nonexpansive mappings in normed space, Proc. amer. math. soc., 97, 695-699, (1986) · Zbl 0622.47054 [16] Alber, Ya.I.; Guerr-Delabriere, S., Principle of weakly contractive maps in Hilbert spaces, (), 7-22 · Zbl 0897.47044 [17] Rhoades, B.E., Some theorems on weakly contractive maps, Nonlinear anal., 47, 4, 2683-2693, (2001) · Zbl 1042.47521 [18] Bae, S., Fixed point theorems for weakly contractive multivalued maps, J. math. anal. appl., 284, 690-697, (2003) · Zbl 1033.47038 [19] Beg, I.; Abbas, M., Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed point theory appl., 2006, 1-7, (2006), (Article ID 74503) · Zbl 1133.54024
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