Hyers-Ulam stabilities for mth differential operators on H²

In this paper, we introduce certain operators T-lambda(m) and T-phi(m) on weighted Hardy spaces H-beta(2), and in the following, we investigate their boundedness on H-beta(2). After that, we prove the Hyers-Ulam stability for certain operators on weighted Hardy spaces H-beta(2). Moreover, we show under what conditions these concepts are stable and unstable by using some examples. Finally, we investigate how differential operators are stable by using different sequences in a corollary and an example.