A Remark on the Functional Equation ... (xi) = ....
A simple functional operator.
A simultaneous system of functional inequalities and mappings which are weakly of a constant sign.
A stability of the generalized sine functional equations. II.
About solutions of a functional equation.
Abstract separation theorems of Rodé type and their applications
Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.
Addition Formulae for Field-Valued Continuous Functions on Topological Groups.
Addition theorems and related geometric problems of group representation theory
The Levi-Civita functional equation (g,h ∈ G), for scalar functions on a topological semigroup G, has as the solutions the functions which have finite-dimensional orbits in the right regular representation of G, that is the matrix elements of G. In considerations of some extensions of the L-C equation one encounters with other geometric problems, for example: 1) which vectors x of the space X of a representation have orbits O(x) that are “close” to a fixed finite-dimensional subspace? 2) for...
Additive and convex functions in linear topological space.
Additive f-bimorphisms and Cosine Type Equations
Additive functional inequalities in Banach modules.
Additive functions modulo a countable subgroup of ℝ
We solve the mod G Cauchy functional equation f(x+y) = f(x) + f(y) (mod G), where G is a countable subgroup of ℝ and f:ℝ → ℝ is Borel measurable. We show that the only solutions are functions linear mod G.
Additive selections of superadditive set-valued functions.
Almost Trivial Groupoids
An algebraic functional equation
An existence and stability theorem for a class of functional equations.
Consider the class of functional equationsg[F(x,y)] = H[g(x),g(y)],where g: E --> X, f: E x E --> E, H: X x X --> X, E is a set and (X,d) is a complete metric space. In this paper we prove that, under suitable hypotheses on F, H and ∂(x,y), the existence of a solution of the functional inequalityd(f[F(x,y)],H[f(x),f(y)]) ≤ ∂(x,y),implies the existence of a solution of the above equation.
An expanded class of parametric partial linear complex vector functional equations.
Analogs of Bernoulli polynomials in fields Zp.
Approximate behavior of bi-quadratic mappings in quasinormed spaces.
Approximate tri-quadratic functional equations via Lipschitz conditions
In this paper, we consider Lipschitz conditions for tri-quadratic functional equations. We introduce a new notion similar to that of the left invariant mean and prove that a family of functions with this property can be approximated by tri-quadratic functions via a Lipschitz norm.