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)
Hyperstability of a class of linear functional equations. (English) Zbl 1004.39022
First the following result is offered: Suppose that $M: ]0,1]\to \Bbb{R}$ is multiplicative and assumes a value greater than 1, and that $f:]0,1]\to \Bbb{R}$ satisfies $|f(xy)-M(x)f(y)-M(y)f(x)|\leq \varepsilon$ for some $\varepsilon\geq 0$. Then $f(xy)-M(x)f(y)-M(y)f(x)=0$ $(x,y\in ]0,1])$. The rest of the paper offers similar and more general results for equations of the form $f(x)+f(y)=\sum_{k=1}^n f[sg_k (t)]/n$ on a semigroup ($f$ maps the semigroup into a real normed space, $g_1,\dots,g_n$ are pairwise distinct automorphisms of the semigroup, forming a group under composition).
Reviewer: J.Aczél (Waterloo)

39B72Systems of functional equations and inequalities
39B52Functional equations for functions with more general domains and/or ranges
20M20Semigroups of transformations, etc.
Full Text: EuDML