zbMATH — the first resource for mathematics

A fixed point theorem for contractive-type fuzzy mappings. (English) Zbl 0831.54036
The authors introduce the concept of contractive-type fuzzy mappings. Under suitable conditions, some existence theorems of fixed points for contractive-type fuzzy mapping on complete metric linear space are proved, which generalize the corresponding results of S. Heilpern [J. Math. Anal. Appl. 83, 566-569 (1981; Zbl 0486.54006)].

MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54A40 Fuzzy topology 47H10 Fixed-point theorems
Keywords:
contractive-type fuzzy mapping
Full Text:
References:
 [1] Bose, R.K.; Sahani, D., Fuzzy mappings and fixed point theorems, Fuzzy sets and systems, 21, 53-58, (1987) · Zbl 0609.54032 [2] Butnariu, D., Fixed points for fuzzy mappings, Fuzzy sets and systems, 7, 191-207, (1982) · Zbl 0473.90087 [3] Butnariu, D., A fixed point theorem and its application to fuzzy games, Revenue roumaine math. pures appl., 24, 10, 1424-1432, (1979) · Zbl 0437.54039 [4] Chang, C.L., Fuzzy topological spaces, J. math. anal. appl., 24, 182-190, (1968) · Zbl 0167.51001 [5] Shih-sen, Chang; Nan-jing, Huang, Fixed point theorems for generalized fuzzy mappings, Acta of engineering math, 2, 135-137, (1984), (in Chinese) [6] Shih-sen, Chang, Fixed point theorems for fuzzy mappings, Kexue tongbao, 14, 833-836, (1984), (in Chinese) [7] Chen, M.P.; Shin, M.H., Fixed point theorems for point-to-point and point-to-set maps, J. math. anal. appl., 71, 515-524, (1979) · Zbl 0439.47047 [8] Chitra, A., A note on the fixed points of fuzzy maps on partially ordered topological spaces, Fuzzy sets and systems, 19, 305-308, (1986) · Zbl 0601.54058 [9] Heilpern, S., Fuzzy mappings and fixed point theorem, J. math. anal. appl., 83, 566-569, (1981) · Zbl 0486.54006 [10] Husain, T.; Latif, Abdul, Fixed points of multivalued nonexpansive maps, Int. J. math. & math. sci., 14, 3, 421-430, (1991) · Zbl 0736.54030 [11] Kelley, J.I., General topology, (1955), D. Van Nostrand Princeton, NJ [12] Nadler, S.B., Multi-valued contraction mappings, Pacific J. math., 30, 475-488, (1969) · Zbl 0187.45002 [13] Som, T.; Mukherjee, R.N., Some fixed point theorems for fuzzy mappings, Fuzzy sets and systems, 33, 213-219, (1989) · Zbl 0685.54030 [14] Weiss, M.D., Fixed points and induced fuzzy topologies for fuzzy sets, J. math. anal. appl., 50, 142-150, (1975) · Zbl 0297.54004 [15] Zadeh, L.A., Fuzzy sets, Inform. control., 8, 338-353, (1965) · Zbl 0139.24606 [16] Zimmermann, H.-J., Fuzzy set theory — and its applications, (1991), Kluwer Academic Publishers Dordrecht · Zbl 0719.04002
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.