A note on a generalization of the quadratic functional equation

Brahim Fadli

Résumé


In the present paper, we determine the solutions f : S!H of the generalized quadratic functional equation f (x+s(y))+ f (x+t(y)) = 2 f (x)+2 f (y); x;y 2 S; in terms of additive and symmetric, bi-additive maps, where S is a commutative semigroup, H is an abelian group which is uniquely 2-divisible, and s; t are two involutions of S:

Mots-clés


Functional equation, quadratic, additive function, semigroup.

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