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Fixed point theorems on fuzzy normed linear spaces. (English) Zbl 1111.46059

Summary: Definitions of strongly fuzzy convergent sequences, \(l\)-fuzzy weakly convergent sequences and \(l\)-fuzzy weakly compact sets are given in a fuzzy normed linear space. The concepts of fuzzy normal structures, fuzzy non-expansive mappings, uniformly convex fuzzy normed linear spaces are introduced and fixed point theorems for fuzzy non-expansive mappings are proved.

MSC:

46S40 Fuzzy functional analysis
47S40 Fuzzy operator theory
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
54A40 Fuzzy topology
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References:

[1] Bag, T.; Samanta, S. K., Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11, 3, 687-705 (2003) · Zbl 1045.46048
[2] Bag, T.; Samanta, S. K., Fuzzy bounded linear operators, Fuzzy Sets Syst., 151, 513-547 (2005) · Zbl 1077.46059
[3] T. Bag, S.K. Samanta, Product fuzzy normed linear spaces, J. Fuzzy Math., accepted for publication.; T. Bag, S.K. Samanta, Product fuzzy normed linear spaces, J. Fuzzy Math., accepted for publication. · Zbl 1100.46511
[4] Cheng, S. C.; Mordeson, J. N., Fuzzy linear operator and fuzzy normed linear spaces, Bull. Cal. Math. Soc., 86, 429-436 (1994) · Zbl 0829.47063
[5] Felbin, C., Finite dimensional fuzzy normed linear spaces, Fuzzy Sets Syst., 48, 239-248 (1992) · Zbl 0770.46038
[6] Frigon, M.; O’Regan, D., Fuzzy contractive maps and fuzzy fixed points, Fuzzy Sets Syst., 129, 1, 39-45 (2002) · Zbl 1025.47048
[7] Grabic, M., Fixed points in fuzzy metric spaces, Fuzzy Sets Syst., 27, 3, 385-389 (1988)
[8] Kaleva, O.; Seikala, S., On fuzzy metric spaces, Fuzzy Sets Syst., 12, 215-229 (1984) · Zbl 0558.54003
[9] Katsaras, A. K., Fuzzy topological vector spaces II, Fuzzy Sets Syst., 12, 143-154 (1984) · Zbl 0555.46006
[10] Kirk, W. A., A fixed point theorem for mappings which do not increase distances, Am. Math. Monthly, 72, 1004-1006 (1965) · Zbl 0141.32402
[11] Kramosil, I.; Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetica, 11, 326-334 (1975)
[12] Marudai, M.; Vijayaraju, P., Fixed point theorems for fuzzy mappings, Fuzzy Sets Syst., 135, 3, 402-408 (2003) · Zbl 1028.54011
[13] Subrahmanyam, P. V., A common fixed point theorems in fuzzy metric spaces, Inf. Sci., 83, 3-4, 109-112 (1995) · Zbl 0867.54017
[14] Xiao, J.; Zhu, X., Topological degree theory and fixed point theorems in fuzzy normed linear spaces-*1, Fuzzy Sets Syst., 147, 3, 437-452 (2004) · Zbl 1108.54010
[15] Zikic, T., On fixed point theorems of Gregori and Sapena, Fuzzy Sets Syst., 144, 3, 421-429 (2004) · Zbl 1052.54006
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