zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Fuzzy versions of Hyers-Ulam-Rassias theorem. (English) Zbl 1178.46075
Summary: We introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense.

46S40Fuzzy functional analysis
39B52Functional equations for functions with more general domains and/or ranges
39B82Stability, separation, extension, and related topics
26E50Fuzzy real analysis
46S50Functional analysis in probabilistic metric linear spaces
Full Text: DOI
[1] Amyari, M.; Moslehian, M. S.: Approximately ternary semigroup homomorphisms, Lett. math. Phys. 77, 1-9 (2006) · Zbl 1112.39021 · doi:10.1007/s11005-005-0042-6
[2] Aoki, T.: On the stability of the linear transformation in Banach spaces, J. math. Soc. Japan 2, 64-66 (1950) · Zbl 0040.35501 · doi:10.2969/jmsj/00210064
[3] Baak, C.; Moslehian, M. S.: Stability of J*-homomorphisms, Nonlinear anal. --- TMA 63, 42-48 (2005) · Zbl 1085.39026 · doi:10.1016/j.na.2005.04.004
[4] Bag, T.; Samanta, S. K.: Finite dimensional fuzzy normed linear spaces, J. fuzzy math. 11, No. 3, 687-705 (2003) · Zbl 1045.46048
[5] Bag, T.; Samanta, S. K.: Fuzzy bounded linear operators, Fuzzy sets and systems 151, 513-547 (2005) · Zbl 1077.46059 · doi:10.1016/j.fss.2004.05.004
[6] Cheng, S. C.; Mordeson, J. N.: Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta math. Soc. 86, 429-436 (1994) · Zbl 0829.47063
[7] Czerwik, S.: Functional equations and inequalities in several variables, (2002) · Zbl 1011.39019
[8] Felbin, C.: Finite dimensional fuzzy normed linear space, Fuzzy sets and systems 48, 239-248 (1992) · Zbl 0770.46038 · doi:10.1016/0165-0114(92)90338-5
[9] Găvruta, P.: A generalization of the Hyers -- Ulam -- rassias stability of approximately additive mappings, J. math. Anal. appl. 184, 431-436 (1994) · Zbl 0818.46043 · doi:10.1006/jmaa.1994.1211
[10] Hyers, D. H.: On the stability of the linear functional equation, Proc. nat. Acad. sci. USA 27, 222-224 (1941) · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222
[11] Hyers, D. H.; Isac, G.; Rassias, Th.M.: Stability of functional equations in several variables, (1998) · Zbl 0907.39025
[12] Jung, S. -M.: Hyers -- Ulam -- rassias stability of functional equations in mathematical analysis, (2001) · Zbl 0980.39024
[13] Katsaras, A. K.: Fuzzy topological vector spaces II, Fuzzy sets and systems 12, 143-154 (1984) · Zbl 0555.46006 · doi:10.1016/0165-0114(84)90034-4
[14] Kramosil, I.; Michalek, J.: Fuzzy metric and statistical metric spaces, Kybernetica 11, 326-334 (1975) · Zbl 0319.54002
[15] Krishna, S. V.; Sarma, K. K. M.: Separation of fuzzy normed linear spaces, Fuzzy sets and systems 63, 207-217 (1994) · Zbl 0849.46058 · doi:10.1016/0165-0114(94)90351-4
[16] Mirzavaziri, M.; Moslehian, M. S.: A fixed point approach to stability of a quadratic equation, Bull. braz. Math. soc. 37, No. 3, 361-376 (2006) · Zbl 1118.39015 · doi:10.1007/s00574-006-0016-z
[17] Moslehian, M. S.: Approximately vanishing of topological cohomology groups, J. math. Anal. appl. 318, No. 2, 758-771 (2006) · Zbl 1098.39020 · doi:10.1016/j.jmaa.2005.06.018
[18] Rassias, Th.M.: On the stability of the linear mapping in Banach spaces, Proc. amer. Math. soc. 72, 297-300 (1978) · Zbl 0398.47040 · doi:10.2307/2042795
[19] Ulam, S. M.: Problems in modern mathematics, (1964) · Zbl 0137.24201
[20] Xiao, J. -Z.; Zhu, X. -H.: Fuzzy normed spaces of operators and its completeness, Fuzzy sets and systems 133, 389-399 (2003) · Zbl 1032.46096 · doi:10.1016/S0165-0114(02)00274-9
[21] A.K. Mirmostafaee, M. Mirzavaziri, M.S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems (2007), doi:10.1016/j.fss.2007.07.011. · Zbl 1179.46060