Generalized hyperstability of a Drygas functional equation on a restricted domain using Brzdęk’s fixed point theorem

Abstract

Motivated by the notion of Ulam stability, we investigate the generalized hyperstability results for the Drygas functional equation $$\begin{array}{c}\hfill f(x+y)+f(x-y)=2f(x)+f(y)+f(-y),\end{array}$$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 Szczawińska [29].