On the superstability of generalized d’Alembert harmonic functions
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 15 (2016)
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The aim of this paper is to study the superstability problem of the d’Alembert type functional equationf(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) 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.
Keywords:
stability, d’Alembert functional equation
EL-Fassi, Iz-iddine. On the superstability of generalized d’Alembert harmonic functions. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 15 (2016). http://geodesic.mathdoc.fr/item/AUPCM_2016_15_a5/
@article{AUPCM_2016_15_a5,
author = {EL-Fassi, Iz-iddine},
title = {On the superstability of generalized {d{\textquoteright}Alembert} harmonic functions},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
year = {2016},
number = {15},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AUPCM_2016_15_a5/}
}