Results 261 to 270 of about 4,706,970 (298)

Functional Equations and Distribution Functions

Results in Mathematics, 1994
Let \(a \in (0,1)\), \(N \in \mathbb{N} \backslash \{1\}\) and \(- 1 = \beta_0 \leq \beta_1 \leq \dots \leq \beta_{N - 1} = 1\). Then the functional equation \[ f(x) = {1 \over N} \sum^{N - 1}_{k = 0} f \left( {x - \beta_k \over a} \right) \] has a unique bounded solution \(f : \mathbb{R} \to \mathbb{R}\) vanishing on \((- \infty, -1/(1 - a))\) and ...
Borwein, Jonathan M., Girgensohn, Roland
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On the Robustness of Functional Equations

SIAM Journal on Computing, 1999
Summary: We study the general question of how characteristics of functional equations influence whether or not they are robust. We isolate examples of properties which are necessary for the functional equations to be robust. On the other hand, we show other properties which are sufficient for robustness.
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On Wilson’s functional equations

Aequationes mathematicae, 2014
This paper concerns mainly a variant of Wilson's functional equation. It is shown that the solutions can be expressed in terms of characters, additive functions and matrix-elements of irreducible 2-dimensional representations of the underlying group. So the theory is part of the harmonic analysis on groups.
Ebanks, Bruce, Stetkaer, Henrik
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ON FUNCTIONAL EQUATIONS OF DIRICHLET FUNCTIONS

Mathematics of the USSR-Izvestiya, 1967
The paper adduces a theorem of a general form on functional equations of the Dirichlet functions, as well as certain of its corollaries.
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On Fréchet’s functional equation

Monatshefte für Mathematik, 2013
The paper is devoted to the basic theorem on polynomials, originally proved by \textit{D. Ž. Đoković} [Ann. Pol. Math. 22, 189--198 (1969; Zbl 0187.39903)], which states that a function \(f: G\to\mathbb{C}\), defined on an abelian group \(G\), is a generalized polynomial of degree at most \(n\), i.e., satisfies Fréchet's equation \[ \Delta_{y_1,y_2 ...
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LINEAR FUNCTIONAL EQUATIONS

Mathematics of the USSR-Izvestiya, 1978
Necessary and sufficient conditions are found for the existence and uniqueness of local solutions of multidimensional linear functional equations of the form . Sufficient conditions for local solvability are also obtained for equations with variable coefficients.Bibliography: 5 titles.
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A Functional Equation for the Cosine

Canadian Mathematical Bulletin, 1968
It is known [3], [5] that, the complex-valued solutions of(B)(apart from the trivial solution f(x)≡0) are of the form(C)(D)In case f is a measurable solution of (B), then f is continuous [2], [3] and the corresponding ϕ in (C) is also continuous and ϕ is of the form [1],(E)In this paper, the functional equation(P)where f is a complex-valued, measurable
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A Functional Equation For Implication

The Mathematical Gazette, 1967
Since all truth functions in two-valued logic may be represented by polynomials in the arithmetic of residues modulo 2, the question which R. Sibson raises in note 3127 may be expressed in the following form : Find all polynomials Φ ( p, q ) such that
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Systems of functional equations

Random Structures & Algorithms, 2000
In this paper ``functional equation'' is an equation of particular form from which an implicit unknown function is to be determined. To be exact, the author looks for analytic solutions (complex variables are written in italics, vector variables and vector valued functions with \(n\) complex components are set in bold face) \({\mathbf y}={\mathbf g}(x,{
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On a Functional Differential Equation

IMA Journal of Applied Mathematics, 1971
Fox, L., Mayers, D. F., Ockendon, J. R., Tayler, A. B.   +3 more
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