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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.
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Rocznik
Tom
Strony
395--408
Opis fizyczny
Bibliogr. 10 poz.,
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- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland, szostok@ux2.math.us.edu.pl
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bwmeta1.element.baztech-article-BAT2-0001-1156