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)
Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces. (English) Zbl 1204.39028

Let G be an additive group and X a complete non-Archimedean normed space. Let the function f:GX satisfy the functional equation


for all x,yG. In this paper, the authors study the Hyers-Ulam-Rassias stability of the above functional equation in non-Archimedean spaces.

39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
[1]Ulam, S. M.: Problems in modern mathematics, (1940)
[2]Hyers, D. H.: On the stability of the linear functional equation, Proc. natl. Acad. sci. 27, 222-224 (1941) · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222
[3]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
[4]Gajda, Z.: On stability of additive mappings, Internat. J. Math. math. Sci. 14, 431-434 (1991) · Zbl 0739.39013 · doi:10.1155/S016117129100056X
[5]Gavruta, 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
[6]Grabiec, A.: The generalized Hyers-Ulam stability of a class of functional equations, Publ. math. Debrecen. 48, 217-235 (1996)
[7]Hyers, D. H.; Isac, G.; Rassias, Th.M.: Stability of functional equation in several variables, (1998)
[8]Isac, G.; Rassias, Th.M.: On the Hyers-Ulam stability of ψ-additive mappings, J. approx. Theory 72, 131-137 (1993) · Zbl 0770.41018 · doi:10.1006/jath.1993.1010
[9]Jung, S. M.: Hyers–Ulam–rassias stability of functional equations in mathematical analysis, (2001) · Zbl 0980.39024
[10]Rassias, Th.M.: On the stability of functional equations and a problem of Ulam, Acta math. Appl. 62, 23-130 (2000) · Zbl 0981.39014 · doi:10.1023/A:1006499223572
[11]Jun, K. W.; Kim, H. M.: The generalized Hyers–Ulam–rassias stability of a cubic functional equation, J. math. Anal. appl. 274, No. 2, 267-278 (2002) · Zbl 1021.39014 · doi:10.1016/S0022-247X(02)00415-8
[12]Park, W.; Bae, J.: On a bi-quadratic functional equation and its stability, Nonlinear anal. TMA 62, No. 4, 643-654 (2005) · Zbl 1076.39027 · doi:10.1016/j.na.2005.03.075
[13]Gordji, M. Eshaghi; Savadkouhi, M. Bavand: Stability of cubic and quartic functional equations in non-Archimedean spaces, Acta appl. Math. 110, 1321-1329 (2010) · Zbl 1192.39018 · doi:10.1007/s10440-009-9512-7
[14]M. Eshaghi Gordji, A. Ebadian, S. Zolfaghari, Stability of a functional equation deriving from cubic and quartic functions, Abstract and Applied Analysis, Volume 2008, Article ID 801904, 17 pages. · Zbl 1160.39334 · doi:10.1155/2008/801904
[15]Chung, J. K.; Sahoo, P. K.: On the general solution of a quartic functional equation, Bull. korean math. Soc. 40, No. 4, 565-576 (2003) · Zbl 1048.39017 · doi:10.4134/BKMS.2003.40.4.565
[16]Lee, S.; Im, S.; Hwang, I.: Quartic functional equations, J. math. Anal. appl. 307, No. 2, 387-394 (2005) · Zbl 1072.39024 · doi:10.1016/j.jmaa.2004.12.062
[17]Najati, A.: On the stability of a quartic functional equation, J. math. Anal. appl. 340, No. 1, 569-574 (2008) · Zbl 1133.39030 · doi:10.1016/j.jmaa.2007.08.048
[18]Park, C.: On the stability of the orthogonally quartic functional equation, Bull. iranian math. Soc. 31, No. 1, 63-70 (2005) · Zbl 1117.39020
[19]Moslehian, M. S.; Rassias, Th.M.: Stability of functional equations in non-Archimedean spaces, Applicable anal. Discrete math. 1, 325-334 (2007)
[20]Gordji, M. Eshaghi; Khodaei, H.: Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces, Nonlinear anal. TMA 71, 5629-5643 (2009) · Zbl 1179.39034 · doi:10.1016/j.na.2009.04.052