Generalized hyperstability of a Drygas functional equation on a restricted domain using Brzdek's fixed point theorem
Motivated by the notion of Ulam stability, we investigate the generalized hyperstability results for the Drygas functional equation \begin{aligned} f(x+y)+f(x y)=2f(x)+f(y)+f( y) \end{aligned}$f(x+y)+f(x y)=2f(x)+f(y)+f( y),on a restricted domain. The method is based on a quite recent fixed point theorem (cf. [6, Theorem 1] in some functions spaces. We derive from them some characterizations of inner product spaces. Our results are improvements and generalizations of the main results of Piszczek and Szczawinska [29]