Abstract
In this paper, we introduce certain operators Tλm and Tφm on weighted Hardy spaces Hβ2, and in the following, we investigate their boundedness on Hβ2. After that, we prove the Hyers–Ulam stability for certain operators on weighted Hardy spaces Hβ2. 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.
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