MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS

doi:10.1016/S0252-9602(12)60030-7

Abstract

Abstract:

Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the so-called multivariate weighted Bernstein, Nikol’skiÏ, and Ul’yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol’skiÏ-type and Ul’yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.

Key words: Bernstein-type inequality, Nikol’skiÏ-type inequality, Ul’yanov-type inequal-ity, approximation

CLC Number:

41A17

CAO Fei-Long, LIN Shao-Bo. MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS[J].Acta mathematica scientia,Series B, 2012, 32(2): 471-482.

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