光盘上某些正线性算子的稳定性
Stability of Some Positive Linear Operators on Compact Disk
摘要：
最近，Popa和Rasa [18，19]证明了定义在[0，1]上的一些经典算子的（不）稳定性，并找到了当正线性算子在Hyers-Ulam意义下稳定时的最佳常数.本文证明了紧致盘上复Bernstein-Schurer算子、复Kantrovich-Schurer算子和Lorentz算子的Hyers-Ulam（in）稳定性。当算子在Hyers和Ulam意义下是稳定的时，我们找到了相应算子的Hyers-Ulam稳定常数的下确界。
英文摘要：
Recently, Popa and Rasa [18,19] have shown the (in)stability of some classical operators defined on [0,1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ulam. In this paper we show Hyers-Ulam (in)stability of complex Bernstein-Schurer operators, complex Kantrovich-Schurer operators and Lorentz operators on compact disk. In the case when the operator is stable in the sense of Hyers and Ulam, we find the infimum of Hyers-Ulam stability constants for respective operators.
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