On the alienation of the exponential Cauchy equation and the Hosszú equation
| Autor: | Gyula Maksa, Maciej Sablik |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics Mathematical analysis 010103 numerical & computational mathematics 01 natural sciences Exponential function Combinatorics Functional equation Discrete Mathematics and Combinatorics 0101 mathematics Connection (algebraic framework) Cauchy's equation Mathematics |
| Zdroj: | Aequationes mathematicae. 90:57-66 |
| ISSN: | 1420-8903 0001-9054 |
| DOI: | 10.1007/s00010-015-0358-y |
| Popis: | In this paper, we give all the solutions \({g,h:\mathbb{R}\to\mathbb{R}}\) (the reals) of the functional equation $$g(x)g(y)-g(x+y)=h(x+y-xy)-h(x)-h(y)+h(xy) \quad(x,y\in\mathbb{R}),$$ supposing additionally that h is continuous. This result is in connection with the alienation of the exponential Cauchy equation g(x + y) = g(x)g(y) and the Hosszu equation h(x + y−xy) + h(xy) = h(x) + h(y), namely it turns out that these equations are alien provided that h is continuous. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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