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On the Rate of Approximation of q-Bernstein Operators and Baskakov Operators

Author: LinDiWang
Tutor: ZengXiaoMing
School: Xiamen University
Course: Basic mathematics
Keywords: q-Bernstein operators Baskakov operators Rate of approximation
CLC: O177
Type: Master's thesis
Year: 2009
Downloads: 57
Quote: 2
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Abstract


In this paper,we study the rate of approximation of q-Bernstein operators and Baskakov operators.The paper is organized as follows:In chapter 1 we give a brief review of approximation theory of operators (approximation by operators),and present the corresponding research background.In chapter 2 by means of kinds of smooth modules and analysis methods,we investigate the rate of convergence of q-Bernstein operators for continuous functions,differentiable functions and Lipschitz functions. We obtain the control constant and the results are better than the results of Phillips[16].In chapter 3 by using probabilistic methods and analysis methods we study pointwise approximation for bounded functions by Baskakov operators.Our investigations subsume the case of functions of bounded variation as special case and improve Guo and Khan’s result[12]by giving a better asympotic estimate.In chapter 4 by means of the decomposition technique of Bojanic and Cheng together with some analysis methods we study rates of convergence of sequence of integral Baskakov operators for a class absolutely continuous functions.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis
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