ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 69,   1   (2000)
pp.   127-135

THE STABILITY OF THE EQUATION $f(xy)-f(x)-f(y)= 0$ ON GROUPS
V. FA IZIEV

Abstract.  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.

AMS subject classification.  20M15, 20M30
Keywords.  Equation, stability, pseudocharacter, group