Notes on f-hom-ders associated with a system of additive functional equations in unital algebras

The following system of additive functional equations ۲f(x+y)=g(x)+g(y), g(x+y)=۲f(y-x)+۴f(x) in a Banach algebra was investigated by Paokanta et al. [S. Paokanta, M. Dehghanian, C. Park and Y. Sayyari, System of additive functional equations in Banach algebras (preprint)]. By using the system (A), Paokanta et al. [S. Paokanta, M. Dehghanian, C. Park and Y. Sayyari, System of additive functional equations in Banach algebras (preprint)] also investigated the notion of an f-hom-der in Banach algebras. In this note, we first show that the system of additive functional equations (A) is equivalent to an additive functional equation and then some aspects related to f-hom-ders are discussed. Finally, we present stability results of f-hom ders associated with the system of additive functional equations (A).

Keywords:

f-hom-der , unital algebra , Banach algebra , system of additive functional equations , stability result