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 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].