zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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 additive and quadratic functional equation in non-Archimedean Banach modules. (English) Zbl 1218.39026

The stability problem of functional equations originated from a question of S. M. Ulam [A collection of mathematical problems. New York and London: Interscience Publishers (1960; Zbl 0086.24101)] concerning the stability of group homomorphisms. D. H. Hyers [Proc. Natl. Acad. Sci. USA 27, 222–224 (1941; Zbl 0061.26403)] gave a first affirmative partial answer to the question of Ulam for Banach spaces.

The authors prove the Hyers-Ulam stability of the additive-quadratic functional equation

f(x+2y)+f(x-2y)+8f(y)=2f(x)+4f(2y)

in non-Archimedean Banach modules over a unital Banach algebra.

The definition of non-Archimedean Banach module over a Banach algebra is not given.

MSC:
39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
46B03Isomorphic theory (including renorming) of Banach spaces
46H25Normed modules and Banach modules, topological modules
46S10Functional analysis over fields (not , , or quaternions)