Journal ArticleDOI
Functional equations on restricted domains
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This article is published in Aequationes Mathematicae.The article was published on 1978-02-01. It has received 55 citations till now.read more
Citations
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Journal ArticleDOI
The stability of Homomorphisms and Amenability, with applications to functional equations.
TL;DR: In this article, the connection between the stability of homomorphisms and the amenability of the group where they are defined has been investigated and a necessary and sufficient condition for amenability in terms of stability is proved.
Book ChapterDOI
Conditional functional equations and orthogonal additivity
TL;DR: In this paper, some examples of classes of conditional equations coming from information theory, geometry and from the social and behavioral sciences are presented, and the classical case of the Cauchy equation on a restricted domain Ω is extensively discussed.
Journal ArticleDOI
Stability of an alternative functional equation
TL;DR: In this paper, the stability of the following alternative functional equation f (x + y ) + f ( x + y) + f( x )+ f ( y ) ≠ 0 ⟹ f(x+ y ) = f(ex + y ), f(ax + y), f(y) = f (ex + x), f (y) + x ) + y, f (ax) + y).
Journal ArticleDOI
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. III. Foundations for the k-Dimensional Case with Applications to k=2
TL;DR: In this article, the authors present a general regular solution to Cauchy's additive functional equation on bounded convex domains, which provides a k-dimensional generalization of the so-called interval lemma, allowing to deduce affine properties of the function from certain additivity relations.
Journal ArticleDOI
A statistical fatigue model covering the tension and compression Wöhler fields
Enrique Castillo,Alfonso Fernández-Canteli,Roland Koller,María Luisa Ruiz-Ripoll,María Luisa Ruiz-Ripoll,Alvaro Garcia,Alvaro Garcia +6 more
TL;DR: The model extends an existing model to the case of σ max being tension and σ min being tension or compression, and is derived based on physical, statistical and compatibility conditions, thus, eliminating the selection of arbitrary functions.
References
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Journal ArticleDOI
Lectures on Functional Equations and their Applications.
Journal ArticleDOI
On the Distribution Function of Additive Functions
TL;DR: In this article, it was shown that the existence of the distribution function does not depend on the values f(p), a > 1, and cannot be destroyed by the behavior of f (p) on a sequence of primes r where Y, 1/ri <.