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Cauchy’s functional equation and extensions: Goldie’s equation and inequality, the Gołąb–Schinzel equation and Beurling’s equation [PDF]
, 2014 The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study this, and its ...
N. Bingham, A. Ostaszewski
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On Fréchet’s functional equation
Monatshefte für Mathematik, 2014The 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 ...
L. Székelyhidi
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Fuzzy stability of a rational functional equation and its relevance to system design
International Journal of General Systems, 2018This study demonstrates the solution and various stabilities of a rational functional equation involving two variables by means of fixed point tactic in the vicinity of Felbin's type fuzzy normed spaces.
B. V. S. Kumar, H. Dutta
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Functional Equations and Distribution Functions
Results in Mathematics, 1994Let \(a \in (0,1)\), \(N \in \mathbb{N} \backslash \{1\}\) 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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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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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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On Wilson’s functional equations
Aequationes mathematicae, 2014This 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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2002
Abstract It sometimes happens that theories in psychology or other empirical sciences are formalized by equations involving unknown functions. For instance, the theorist may be reluctant to make specific assumptions regarding the form of the functions involved in a mathematical model.
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Abstract It sometimes happens that theories in psychology or other empirical sciences are formalized by equations involving unknown functions. For instance, the theorist may be reluctant to make specific assumptions regarding the form of the functions involved in a mathematical model.
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Functions and Functional Equations
2015The concept of function is one of the most important in mathematics. A function is a relation between elements of two sets X and Y , which we denote by f : X → Y , that satisfies.
Radmila Bulajich Manfrino +2 more
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JP Journal of Algebra Number Theory and Applications, 2020
D. Villa-Hernández
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D. Villa-Hernández
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