Geodesic
THE STABILITY OF THE EQUATION $f(xy)-f(x)-f(y)= 0$ ON GROUPS
Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 1 
V. FA Iziev. THE STABILITY OF THE EQUATION $f(xy)-f(x)-f(y)= 0$ ON GROUPS. Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2000_69_1_a11/
@article{AMUC_2000_69_1_a11,
     author = {V. FA Iziev},
     title = {THE {STABILITY} {OF} {THE} {EQUATION} $f(xy)-f(x)-f(y)= 0$ {ON} {GROUPS}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2000},
     volume = {69},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2000_69_1_a11/}
}
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Voir la notice de l'article provenant de la source Comenius University

Let $G$ be a group and let $E$ be a Banach space. Suppose that a mapping $f\:G\to E$ satisfies the relation $||f(xy)- f(x)- f(y) ||\le c $ for some $c>0$ and any $ x,y\in G$. The problem of existence of mappings $l \: G\to E$ such that the following relations hold 1) $l(xy)- l(x)- l(y) =0$ for any $ x,y\in G$; 2) the set $\\;||l(x) -f(x)||\; ;\forall x,y \in G $ is bounded is considered.