On approximate solution of Drygas functional equation according to the Lipschitz criteria

Let G be an Abelian group with a metric d and E be a normed space. For any f : G -> E we define the Drygas difference of the function f by the formula Lambda f(x, y):= 2f(x) + f(y) + f(-y) - f(x + y) - f(x - y) for all x, y is an element of G. In this article, we prove that if Lambda f is Lipschitz, then there exists a Drygas function D : G -> E such that f-D is Lipschitz with the same constant. Moreover, some results concerning the approximation of the Drygas functional equation in the Lipschitz norms are presented.