A generalization of Drygas functional equation

which can be reduced to the following equation (see [21], Remark 9.2, p.131)(1.1) f(x+y)+f(x−y)=2f(x)+f(y)+f(−y),x,y∈Rwhere R denotes the set of real numbers.This equation is known in the literature as Drygas equation and is ageneralization of the quadratic functional equation(1.2) f(x+y)+f(x−y)=2f(x)+2f(y),x,y∈R.The general solution of Drygas equation was given by Ebanks, Kannappanand Sahoo in [10]. It has the formf(x)=A(x)+Q(x),where A: R −→R is an additive function and Q: R −→R is a quadraticfunction, see also [17]. A set-valued version of Drygas equation was consid-ered by Smajdor in [23]. The Drygas functional equation on an arbitrarygroup G takes the form(1.3) f(xy)+f(xy