Bag, T.; Samanta, S. K. Fixed point theorems on fuzzy normed linear spaces. (English) Zbl 1111.46059 Inf. Sci. 176, No. 19, 2910-2931 (2006). 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. Cited in 1 ReviewCited in 13 Documents 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 Keywords:fuzzy convergence; fuzzy compact; fuzzy normal structure; fuzzy nonexpansive mapping; uniformly convex fuzzy normed linear space; fixed point PDFBibTeX XMLCite \textit{T. Bag} and \textit{S. K. Samanta}, Inf. Sci. 176, No. 19, 2910--2931 (2006; Zbl 1111.46059) Full Text: DOI 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 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.