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.


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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|