On the functional equationf(x) g(y) = p(x + y) q(x/y)

Aequationes mathematicae -     

The Functional Equationf(x+y−xy)+f(xy)=f(x)+f(y)

Aequationes mathematicae -     

On the functional equation x + f(y + f(x))=y + f(x + f(y))

For an abelian group (G, + ,0) we consider the functional equation $$f : G \to G, x + f(y + f(x)) = y + f(x + f(y)) \quad (\forall x, y \in G), \quad\quad\qquad (1)$$ most times together with the condition $$f(0) = 0.\qquad\qquad\qquad\qquad\qquad (0)$$ Our main question is whether a solution of ${(1) \wedge (0)}$ must be additive, i.e., an endomorphism of G. We shall answer this question in the negative (Example 3.14) Rätz (Aequationes Math 81:300, 2011).     

On the functional equation $$f(x+y)=f(x)+f(y)$$f(x+y)=f(x)+f(y)

Monatshefte für Mathematik - An extension of the linearity of the continuous solutions of the functional equation $$f(x+y)=f(x)+f(y)$$ to measurable functions is presented.     

Das goursat-problem füru xy =f (x,y, u)

Ohne Zusammenfassung     

Das Goursat-Problem füru xy =f(x,y, u)

Ohne Zusammenfassung