| On general Bernstein and Nikol’ski type inequalities |
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| 作者单位： | Department of Mathematics, China Jiliang University, Hangzhou 310018, China |
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| 基金项目： | Supported by the National Science Foundation of China（Grants 90818020 and 60874029） |
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| 摘 要： | The goal of this paper is to establish the relations between general Bernstein and Nikol’ski type inequalities under some weak conditions. From these relations some known classical inequalities are implied. Also, a family of functions equipped with Bernstein type inequality which satisfies Nikol’ski type inequality is found.
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| 关 键 词： | 伯恩斯坦 不等式 函数族 |
On general Bernstein and Nikol’skiî type inequalities |
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| Authors: | Fei-long Cao Shao-bo Lin Bao-lin Zhang |
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| Institution: | Department of Mathematics, China Jiliang University, Hangzhou 310018, China |
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| Abstract: | The goal of this paper is to establish the relations between general Bernstein and Nikol’skiî type inequalities under some weak conditions. From these relations some known classical inequalities are implied. Also, a family of functions equipped with Bernstein type inequality which satisfies Nikol’skiî type inequality is found. |
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| Keywords: | Bernstein inequality Nikol'ski(i) inequality Markov inequality |
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