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摘要: |
讨论了α-Bernstein算子与其逼近函数间的一个关系:若α-Bernstein算子满足Lipschitz连续,那么他逼近的函数也满足Lipschitz连续,反之亦然。而且α-Bernstein 算子保持原来函数的Lipschitz常数。 |
关键词: 函数逼近 α-Bernstein算子 Lipschitz连续 Lipschitz函数 |
DOI: |
分类号:O241.5 |
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目) |
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THE α-BERNSTEIN OPERATOR OF A LIPSCHITZ CONTINUOUS FUNCTION |
Liu zhi,Chen Xiaoyan
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Abstract: |
The relationship between the α-Bernstein operator and its approximation function is discussed in this paper. If the α-Bernstein operator belongs to the class of Lipschitz functions, then its approximation function f (x) also does, and vice versa. Moreover, the α-Bernstein operator can maintain the Lipschitz constant of the original function. |
Key words: function approximation α-Bernstein operators Lipschitz continuity Lipschitz functions |