A generalized Jensen type mapping and its applications
A generalized Jensen type mapping and its applications
Let $X$ and $Y$ be vector spaces. It is shown that a mapping $f : X \rightarrow Y$ satisfies the functional equation (2d+1) f(\frac{\sum_{j=1}^{2d+1} (-1)^{j+1} x_j}{2d+1}) = \sum_{j=1}^{2d+1} (-1)^{j+1} f(x_j) \end{aligned} if and only if the mapping $f : X \rightarrow Y$ is additive, and prove the Cauchy-Rassias stability of …