A characterization of damped and undamped harmonic oscillations by a superposition property II.
A characterization of monomial functions.
A fixed point approach to the stability of a generalized Cauchy functional equation.
A fixed point approach to the stability of an equation of the square spiral.
A functional equation characterizing cubic polynomials and its stability.
A functional equation involving f and .
A functional equation related to an equality of means problem
The functional equation (F(x)-F(y))/(x-y) = (G(x)+G(y))(H(x)+H(y)) where F,G,H are unknown functions is considered. Some motivations, coming from the equality problem for means, are presented.
A Gauss type functional equation.
A general class of iterative equations on the unit circle
A class of functional equations with nonlinear iterates is discussed on the unit circle . By lifting maps on and maps on the torus to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
A model of competition
A competition model is described by a nonlinear first-order differential equation (of Riccati type). Its solution is then used to construct a functional equation in two variables (admitting essentially the same solution) and several iterative functional equations; their continuous solutions are presented in various forms (closed form, power series, integral representation, asymptotic expansion, continued fraction). A constant C = 0.917... (inherent in the model) is shown to be a transcendental number....
A new analogue of Gauss' functional equation.
A note on d'Alembert's functional equation
A note on stability of a linear functional equation of second order connected with the Fibonacci numbers and Lucas sequences.
A note on the convolution theorem for the Fourier transform
In this paper we characterize those bounded linear transformations carrying into the space of bounded continuous functions on , for which the convolution identity holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
A package for symbolic solution of real functional equations of real variables.
A remark on th-order linear functional equations with constant coefficients.
A Remark on the Functional Equation ... (xi) = ....
Abel's equation and regular growth: Variations on a theme by Abel.
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 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.