| 摘要: |
| 本文讨论了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，那么其逼近的函数也满足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:Supported by National Natural Science Foundation of China (11601115). |
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| THE α-BERNSTEIN OPERATOR OF A LIPSCHITZ CONTINUOUS FUNCTION |
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LIU Zhi, WANG Chu-han, CHEN Xiao-yan, TAN Jie-qing
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School of Mathematics, Hefei University of Technology, Hefei 230009, China
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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 |
