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Fixed point theorems for fuzzy mappings. (English) Zbl 1028.54011
The results of R. K. Bose and R. N. Mukherjee from [Tamkang J. Math. 8, 245-248 (1977; Zbl 0402.54050)] concerning fixed points of multivalued mappings are extended for contractive fuzzy mappings in complete metric spaces. Also results of R. K. Bose and D. Sahani from [Fuzzy Sets Syst. 21, 53-58 (1987; Zbl 0609.54032)] are generalized for nonexpansive mappings in normed linear spaces.

MSC:
54A40 Fuzzy topology
54E35 Metric spaces, metrizability
54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] Bose, R.K.; Mukherjee, R.N., Common fixed points of some multivalued mappings, Tamkang J. math., 8, 2, 245-249, (1977)
[2] Bose, R.K.; Sahani, D., Fuzzy mappings and fixed point theorems, Fuzzy sets and systems, 21, 53-58, (1987) · Zbl 0609.54032
[3] Heilpern, S., Fuzzy mappings and fixed point theorems, J. math. anal. appl., 83, 566-569, (1981) · Zbl 0486.54006
[4] Nadler, S.B., Multi-valued contraction mappings, Pacific J. math., 30, 369-380, (1969)
[5] Nguyen, H.T., A note on extension principle for fuzzy sets, J. math. anal. appl., 64, 369-380, (1978) · Zbl 0377.04004
[6] Som, T.; Mukherjee, R.N., Some fixed point theorems for fuzzy mappings, Fuzzy sets and systems, 33, 213-219, (1989) · Zbl 0685.54030
[7] P. Veeramani, On fuzzy numbers, Proceedings of the U.G.C. sponsored National Seminar on Fuzzy Sets and its Applications, Union Christian College, Alwaye, Kerala, India, 1999, pp. 45-46.
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