Communications of the
Korean Mathematical Society CKMS

We consider the Hyers-Ulam-Rassias stability problem $$ \left\|2u\circ \frac A 2 -u\circ P_1 -u\circ P_2 \right\|\le \varepsilon (|x|^p +|y|^p),\quad x, y \in \Bbb R^n $$ for the Schwartz distributions $u$, which is a distributional version of the Hyers-Ulam-Rassias stability problem of the Jensen functional equation $$ \left|2f\left(\frac{x+y} 2 \right) - f(x) - f(y)\right| \le \varepsilon (|x|^p +|y|^p),\quad x, y \in \Bbb R^n $$ for the function $f :\Bbb R^n \to \Bbb C$.

Keywords: stability, Gauss transforms, heat kernel, distributions, tempered distribution, Jensen functional equation

MSC numbers: 39B82, 46F99