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)
A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces. (English) Zbl 1187.46067
Summary: We define a notion for a quasi fuzzy $p$-normed space, then we use the fixed point alternative theorem to establish Hyers-Ulam-Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy $p$-normed space. Later, we show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, control function and the unique quartic mapping which approximates the almost quartic map. Finally, some applications of our results in the stability of quartic mappings from a linear space into a quasi $p$-norm space will be exhibited.

46S40Fuzzy functional analysis
39B82Stability, separation, extension, and related topics
Full Text: DOI
[1] Aoki, T.: Locally bounded linear topological spaces, Proc. imp. Acad. Tokyo 18, 588-594 (1942) · Zbl 0060.26503 · doi:10.3792/pia/1195573733
[2] Bag, T.; Samanta, S. K.: Finite dimensional fuzzy normed linear spaces, J. fuzzy math. 11, No. 3, 687-705 (2003) · Zbl 1045.46048
[3] 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
[4] 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
[5] Diaz, J. B.; Margolis, B.: A fixed point theorem of the alternative for the contractions on generalized complete metric space, Bull. amer. Math. soc. 74, 305-309 (1968) · Zbl 0157.29904 · doi:10.1090/S0002-9904-1968-11933-0
[6] 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
[7] 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
[8] 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
[9] Kramosil, I.; Michalek, J.: Fuzzy metric and statistical metric spaces, Kybernetica 11, 326-334 (1975) · Zbl 0319.54002
[10] 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
[11] D. Mihet, The fixed point method for fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems (2008), doi:10.1016/j.fss.2008.06.014.
[12] Mihet, D.; Radu, V.: On the stability of the additive Cauchy functional equation in random normed spaces, J. math. Anal. appl. 343, 567-572 (2008) · Zbl 1139.39040 · doi:10.1016/j.jmaa.2008.01.100
[13] Mirmostafaee, A. K.; Mirzavaziri, M.; Moslehian, M. S.: Fuzzy stability of the Jensen functional equation, Fuzzy sets and systems 159, 730-738 (2008) · Zbl 1179.46060 · doi:10.1016/j.fss.2007.07.011
[14] Mirmostafaee, A. K.; Moslehian, M. S.: Fuzzy versions of Hyers -- Ulam -- rassias theorem, Fuzzy sets and systems 159, 720-729 (2008) · Zbl 1178.46075 · doi:10.1016/j.fss.2007.09.016
[15] Mirmostafaee, A. K.; Moslehian, M. S.: Fuzzy almost quadratic functions, Results math. 52, 161-177 (2008) · Zbl 1157.46048 · doi:10.1007/s00025-007-0278-9
[16] Mirmostafaee, A. K.; Moslehian, M. S.: Fuzzy approximately cubic mappings, Inform. sci. 78, No. 19, 3791-3798 (2008) · Zbl 1160.46336 · doi:10.1016/j.ins.2008.05.032
[17] V. Radu, The fixed point alternative and the stability of functional equations, in: Seminar on Fixed Point Theory, Cluj-Napoca, Vol. 4, 2003. · Zbl 1051.39031
[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] S.M. Ulam, Some questions in analysis: §1, stability, Problems in Modern Mathematics, Science eds., Wiley, New York, 1964 (Chapter VI). · Zbl 0137.24201