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A short proof of alienation of additivity from quadraticity

In: Tatra Mountains Mathematical Publications, vol. 74, no. 2
Roman Ger
Detaily:
Rok, strany: 2019, 57 - 62
Jazyk: eng
Kľúčové slová:
alienation phenomenon; additive and quadratic mappings; systems of functional equations.
Typ článku: mathematics
Typ dokumentu: Scientific article *.pdf
O článku:
Without the use of pexiderized versions of abstract polynomials theory, we show that on 2-divisible groups the functional equation \[f(x+y) + g(x+y) + g(x-y) = f(x) + f(y) + 2g(x) + 2g(y)\] forces the unknown functions $f$ and $g$ to be additive and quadratic, respectively, modulo a constant. \par Motivated by the observation that the equation \[f(x+y) + f(x2) = f(x) + f(y) + f(x)2\] implies both the additivity and multiplicativity of $f$, we deal also with the alienation phenomenon of equations in a single and several variables.
Ako citovať:
ISO 690:
Ger, R. 2019. A short proof of alienation of additivity from quadraticity. In Tatra Mountains Mathematical Publications, vol. 74, no.2, pp. 57-62. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0019

APA:
Ger, R. (2019). A short proof of alienation of additivity from quadraticity. Tatra Mountains Mathematical Publications, 74(2), 57-62. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0019
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 25. 10. 2019
Verejná licencia:
Licensed under the Creative Commons Attribution-NC-ND4.0 International Public License.