The aim of this paper is to study the superstability problem of the d’Alembert type functional equation f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) for all x, y, z ∈ G, where G is an abelian group and σ : G → G is an endomorphism such that σ(σ(x)) = x for an unknown function f from G into ℂ or into a commutative semisimple Banach algebra.
@article{bwmeta1.element.doi-10_1515_aupcsm-2016-0001,
author = {Iz-iddine EL-Fassi},
title = {On the superstability of generalized d'Alembert harmonic functions},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
volume = {15},
year = {2016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2016-0001}
}
Iz-iddine EL-Fassi. On the superstability of generalized d’Alembert harmonic functions. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 15 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2016-0001/