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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.

Toader, Silvia, Rassias, Themistocles M., Toader, Gheorghe (2001)

International Journal of Mathematics and Mathematical Sciences

A general class of iterative equations on the unit circle

Marek Cezary Zdun, Wei Nian Zhang (2007)

Czechoslovak Mathematical Journal

A class of functional equations with nonlinear iterates is discussed on the unit circle $𝕋^{1}$ . By lifting maps on $𝕋^{1}$ and maps on the torus $𝕋^{n}$ 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

Peter Kahlig (2012)

Applicationes Mathematicae

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.

Haruki, Hiroshi, Rassias, Themistocles M. (1995)

International Journal of Mathematics and Mathematical Sciences

A note on d'Alembert's functional equation

Mohamed Akkouchi (2001)

Annales mathématiques Blaise Pascal

A note on stability of a linear functional equation of second order connected with the Fibonacci numbers and Lucas sequences.

Brzdȩk, Janusz, Jung, Soon-Mo (2010)

Journal of Inequalities and Applications [electronic only]

A note on the convolution theorem for the Fourier transform

Charles S. Kahane (2011)

Czechoslovak Mathematical Journal

In this paper we characterize those bounded linear transformations $T f$ carrying $L^{1} (ℝ^{1})$ into the space of bounded continuous functions on $ℝ^{1}$ , for which the convolution identity $T (f * g) = T f \cdot T g$ 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.

Enrique Castillo, Andres Iglesias (1997)

Aequationes mathematicae

A remark on $k$ th-order linear functional equations with constant coefficients.

Laitochová, Jitka (2006)

Advances in Difference Equations [electronic only]

A Remark on the Functional Equation ... (xi) = ....

J. PFANZAGL, G. LAUBE (1971)

Aequationes mathematicae

Abel's equation and regular growth: Variations on a theme by Abel.

Szekeres, George (1998)

Experimental Mathematics

Addition theorems and related geometric problems of group representation theory

Ekaterina Shulman (2013)

Banach Center Publications

The Levi-Civita functional equation $f (g h) = \sum_{k = 1}^{n} u_{k} (g) v_{k} (h)$ (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 $g \mapsto T_{g}$ have orbits O(x) that are “close” to a fixed finite-dimensional subspace? 2) for...

Additive functions modulo a countable subgroup of ℝ

Nikos Frantzikinakis (2003)

Colloquium Mathematicae

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.

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