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INICIO |
27 de julio de 2024
Some remarks on a problem of C. Alsina.
| Título inglés | Some remarks on a problem of C. Alsina. |
|---|---|
| Título español | Algunas observaciones a un problema de C. Alsina. |
| Autor/es | Matkowski, J. ; Sablik, M. |
| Organización | Dep. Math. Tech. Univ., Findera, Polonia;Dep. Mat. Silesian Univ., Katowice, Polonia |
| Revista | 0210-7821 |
| Publicación | 1986, 10 (3): 199-212, 13 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: [4] phi(f(x)+x) = phi(f(x)) + phi(x), restricted to the graph of the function f, of the type not yet considered. We describe a general solution as well as we give some conditions sufficient for the uniqueness of solutions of [2] and [4]. |
| Clasificación UNESCO | 120208 |
| Palabras clave español | Ecuaciones funcionales ; Ecuación de Cauchy |
| Código MathReviews | MR0957486 |
| Código Z-Math | Zbl 0649.39006 |
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