Hyers-Ulam Stability of Differential Operators on Reproducing Kernel Function Spaces.

In this paper, we investigate the Hyers-Ulam stability of the differential operators $$T_\lambda $$ and D on the weighted Hardy spaces $$H_\beta ^2$$ with the reproducing property. We obtain a necessary and sufficient condition in order that D is stable on $$H_\beta ^2$$ , and construct an example concerning the stability of $$T_\lambda $$ on $$H_\beta ^2$$ . Moreover, we also investigate the Hyers-Ulam stability of the partial differential operators $$D_i$$ on the several variables reproducing kernel space $$H_f^2(\mathbb {B}_d)$$ . [ABSTRACT FROM AUTHOR]