Generalized Hyers–Ulam Stability for General Quadratic Functional Equation in Quasi-Banach Spaces

Abstract

In this paper, we investigate the generalized Hyers–Ulam stability of an n-dimensional quadratic functional equation $$f\bigg{(}\sum \limits_{i=1}^{n}{x}_{ i}\bigg{)} +{ \sum \nolimits }_{1\leq i<j\leq n}f({x}_{i} - {x}_{j}) = n\sum \limits_{i=1}^{n}f({x}_{ i})\qquad (n \geq 2)$$ in quasi-Banach spaces.