Hyers-Ulam-Rassias stability of Jensen's equation and its application

摘要: The Hyers-Ulam-Rassias stability for the Jensen functional equation is investigated, and the result is applied to the study of an asymptotic behavior of the additive mappings; more precisely, the following asymptotic property shall be proved: Let $ X $ and $ Y $ be a real normed space and a real Banach space, respectively. A mapping $ f: X\rightarrow Y $ satisfying $ f (0)= 0$ is additive if and only if $\left\| 2f\left [(x+ y)/2\right]-f (x)-f (y)\right\|\rightarrow 0$ as $\| x\|+\| y\|\rightarrow\infty $. References