Stability of the General Mixed Additive and Quadratic Functional Equation in Quasi Banach Spaces

Prondanai Kaskasem, Chakkrid Klin-eam, Boriwat Noytabtim

Abstract

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the following general mixed additive and quadratic functional equation

$f(\lambda x +y) +f(\lambda x -y) =f(x+y)+f(x-y)+(\lambda -1)[(\lambda +2)f(x)+\lambda f(-x)]$

where $\lambda \in \mathbb{N}$ and $\lambda \neq 1$ in quasi Banach spaces. Moreover, we use contractive subadditive and expansively superadditive function to prove stability of   the general  mixed additive and quadratic functional equation in quasi Banach spaces.