On the superstability of generalized d’Alembert harmonic functions

Iz-iddine EL-Fassi. "On the superstability of generalized d’Alembert harmonic functions." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 15 (2016): 5-13. <http://eudml.org/doc/287162>.

@article{Iz2016,
abstract = {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) \[f(x + y + z) + f(x + y + \sigma (z)) + f(x + \sigma (y) + z) + f(\sigma (x) + y + z) = 4f(x)f(y)f(z)\] 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.},
author = {Iz-iddine EL-Fassi},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {stability; d’Alembert functional equation; d'Alembert functional equation; superstability; abelian group; Banach algebra},
language = {eng},
pages = {5-13},
title = {On the superstability of generalized d’Alembert harmonic functions},
url = {http://eudml.org/doc/287162},
volume = {15},
year = {2016},
}

TY - JOUR
AU - Iz-iddine EL-Fassi
TI - On the superstability of generalized d’Alembert harmonic functions
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2016
VL - 15
SP - 5
EP - 13
AB - 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) \[f(x + y + z) + f(x + y + \sigma (z)) + f(x + \sigma (y) + z) + f(\sigma (x) + y + z) = 4f(x)f(y)f(z)\] 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.
LA - eng
KW - stability; d’Alembert functional equation; d'Alembert functional equation; superstability; abelian group; Banach algebra
UR - http://eudml.org/doc/287162
ER -