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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	35-42
Number of pages	8
Journal	Applied Mathematics
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s11766-010-2114-3
State	Published - Mar 2010
Externally published	Yes

Keywords

Bernstein inequality
Markov inequality
Nikol'skiî inequality

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10.1007/s11766-010-2114-3

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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",

month = mar,

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

language = "英语",

volume = "25",

pages = "35--42",

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AU - Cao, Fei long

AU - Lin, Shao bo

AU - Zhang, Bao lin

PY - 2010/3

Y1 - 2010/3

N2 - 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.

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

U2 - 10.1007/s11766-010-2114-3

DO - 10.1007/s11766-010-2114-3

M3 - 文章

AN - SCOPUS:77949353197

SN - 1005-1031

VL - 25

SP - 35

EP - 42

JO - Applied Mathematics

JF - Applied Mathematics

IS - 1

ER -

On general Bernstein and Nikol'skiî type inequalities

Abstract

Keywords

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