On general Bernstein and Nikol'skiî type inequalities

Fei long Cao; Shao bo Lin; Bao lin Zhang

doi:10.1007/s11766-010-2114-3

On general Bernstein and Nikol'skiî type inequalities

Fei long Cao
, Shao bo Lin
, Bao lin Zhang

China Jiliang University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
页（从-至）	35-42
页数	8
期刊	Applied Mathematics
卷	25
期	1
DOI	https://doi.org/10.1007/s11766-010-2114-3
出版状态	已出版 - 3月 2010
已对外发布	是

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title = "On general Bernstein and Nikol'ski{\^i} type inequalities",

abstract = "The goal of this paper is to establish the relations between general Bernstein and Nikol'ski{\^i} 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{\^i} type inequality is found.",

keywords = "Bernstein inequality, Markov inequality, Nikol'ski{\^i} inequality",

author = "Cao, \{Fei long\} and Lin, \{Shao bo\} and Zhang, \{Bao lin\}",

year = "2010",

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doi = "10.1007/s11766-010-2114-3",

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AB - 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.

KW - Bernstein inequality

KW - Markov inequality

KW - Nikol'skiî inequality

UR - https://www.scopus.com/pages/publications/77949353197

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DO - 10.1007/s11766-010-2114-3

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JO - Applied Mathematics

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On general Bernstein and Nikol'skiî type inequalities

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