In this paper the stability
of the quadratic equation is considered on arbitrary groups.
Since the quadratic equation is stable on Abelian groups, this paper examines the
stability of the quadratic equation on noncommutative groups.
It is shown that the quadratic equation is stable on $n$-Abelian groups
when $n$ is a positive integer. The stability of the quadratic equation is also
established on the noncommutative group $T(2, K)$,
where $K$ is an arbitrary commutative field.
It is proved that every group can be embedded into a group in which the
quadratic equation is stable.
Publié le : 2008-02-15
Classification:
Banach spaces,
$n$-Abelian group,
pseudoquadratic map,
quadratic map,
quasiquadratic map,
quadratic functional equation,
semidirect product of groups,
stability of quadratic functional equation,
wreath product of groups,
20M15,
20M30,
39B82
@article{1203692452,
author = {Fa\u\i ziev, Valeri\u\i\ A. and Sahoo, Prasanna K.},
title = {On the stability of the quadratic equation on groups},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {15},
number = {1},
year = {2008},
pages = { 135-151},
language = {en},
url = {http://dml.mathdoc.fr/item/1203692452}
}
Faĭziev, Valeriĭ A.; Sahoo, Prasanna K. On the stability of the quadratic equation on groups. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp. 135-151. http://gdmltest.u-ga.fr/item/1203692452/