General quadratic functional equations in quasi-β-normed spaces: Solution, superstability and stability

Abstract

Let f: X → Y be a mapping where X is a quasi-α-normed space and Y is a quasi-β-normed space. The following quadratic functional equation (Formula present) (0.1) is introduced and solved by giving its general solution. Moreover, we prove the Hyers-Ulam stability of the functional equation (0.1) by using a direct method.