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On a generalized orthogonal additivity

Szostok T.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 4

395-408

Some relations between the modified version of the orthogonal Cauchy equation and the following more general equation f(x + y) = g ([...]) [f(x) + f(y)] are obtained. Further the Cauchy equation with the right-hand side multiplied by some constant is considered. This equation is assumed for all x,y satisfying the equality [...] = [alpha]. Finally solutions of this cooditional equation in the case of odd functions defined on inner product spaces and [alpha] lying in some interval are determined.