On the general solution and hyperstability of the general radical quintic functional equation in quasi-β-Banach spaces

The goal of this paper is to study the general solution of the following general radical quintic functional equation f ((5)root ax(5) + by(5)) = rf (x) + sf (y) for f a mapping from the field of real numbers into a vector space, where a, b, r, s are fixed nonzero reals. Also, we prove the generalized hyperstability results for the general radical quintic functional equation by using the fixed point theorem (cf. Dung and Hang (2018) [15], Theorem 2.1) in quasi-beta-Banach spaces. Namely, we show, under some weak natural assumptions, functions satisfying the above equation approximately (in some sense) must be actually solutions to it. (C) 2018 Elsevier Inc. All rights reserved.