A generalized mixed type of quartic, cubic, quadratic and additive functional equation
We determine the general solution of the functional equation $f(x + ky) + f(x — ky) = g(x + y) + g(x — y) + h(x) + \tilde{h}(y)$ forfixed integers $k$ with $k \neq 0, \pm 1$ without assuming any regularity condition on the unknown functions $f, g, h, \tilde{h}$. The method used for solving these f...
Gespeichert in:
| Datum: | 2011 |
|---|---|
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2011
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2725 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We determine the general solution of the functional equation $f(x + ky) + f(x — ky) = g(x + y) + g(x — y) + h(x) + \tilde{h}(y)$
forfixed integers $k$ with $k \neq 0, \pm 1$ without assuming any regularity condition on the unknown functions $f, g, h, \tilde{h}$.
The method used for solving these functional equations is elementary but exploits an important result due to Hosszii.
The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi. |
|---|