On the hyperstability of the generalized class of Drygas functional equations on semigroups

The aim of this paper is to offer some hyperstability results for the following functional equation Sigma(lambda is an element of Lambda)f(x lambda center dot y) = Lf(x)+ Sigma(lambda is an element of Lambda)f(lambda.y) (x,y is an element of S), where S is a semigroup, Lambda is a finite subgroup of the group of endomorphisms of S, L is the cardinality of Lambda (i.e. L = card(Lambda)) and f : S -> G such that (G, +) is a L-cancellative abelian group with a metric d. Moreover, we discuss some remarks concerning particular cases of the considered equation and the inhomogeneous equation Sigma(lambda is an element of Lambda)f(x lambda center dot y) = Lf(x)+ Sigma(lambda is an element of Lambda)f(lambda center dot y) + F(x, y) (x,y is an element of S), where F : S x S -> G.