The Hyers?Ulam stability constant for Chebyshevian Bernstein operators
The Hyers?Ulam stability constant for Chebyshevian Bernstein operators
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切比雪夫伯恩斯坦算子的 Hyers?Ulam 稳定性常数
DOI：
10.1016/j.jmaa.2018.03.067
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发表时间：
2018
影响因子：
1.3
通讯作者：
Mazure Marie-Laurence
中科院分区：
文献类型：
--
作者：
Ait-Haddou Rachid;Furihata Daisuke;Mazure Marie-Laurence
在闭有界区间上，给定的具有伯恩斯坦基的扩展切比雪夫空间生成无限多个伯恩斯坦型算子。我们证明所有这些算子都具有相同的 Hyers-Ulam 稳定性常数。该常数是与给定空间相关的广义切比雪夫多项式的贝塞尔系数的绝对值最大值。我们建立了这些 Bernstein 算子关于 Hyers-Ulam 稳定常数的最优性。这些常数的数值计算在两种情况下进行研究：有理算子和 Müntz Bernstein 算子，特别强调它们相对于相关区间和维度高程的行为。
On a closed bounded interval, a given Extended Chebyshev space which possesses a Bernstein basis generates infinitely many operators of the Bernstein-type. We show that all these operators share the same Hyers–Ulam stability constant. This constant is the maximum, in absolute value, of the Bézier coefficients of the generalised Chebyshev polynomial associated with the given space. We establish an optimality property of these Bernstein operators with respect to the Hyers–Ulam stability constant. Numerical computations of these constants are investigated in two cases: rational and Müntz Bernstein operators, with special emphasis on their behaviour with respect to the concerned interval and to dimension elevation.