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推广的Baskakov-Durrmeyer型算子在L_p[0,∞)空间中的逼近(英文) 被引量：2

Approximation for the Generalized Baskakov-Durrmeyer Type Operators in the Space L_p[0,∞)
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摘要 利用Ditzian-Totik模给出并证明了Baskakov-Durrmeyer-Bezier算子在L_p[0,∞)(1≤p≤∞)空间中逼近的正定理、逆定理和等价定理. In this note we give the direct approximation theorem, inverse theorem and equivalence theorem for Baskakov-Durrmeyer-Bézier operators in the space Lp[0,∞）（1 ≤ p ≤ ∞） with Ditzian-Totik modulus.
作者 郭顺生 刘国芬
机构地区 河北师范大学数学与信息科学学院
出处 《数学进展》 CSCD 北大核心 2013年第3期327-338,共12页 Advances in Mathematics（China）
基金 supported by NSFC(No.10801043)
关键词 Baskakov-Durrmeyer-Bezier算子 正逆定理 光滑模 K-泛函 Baskakov-Durrmeyer-Bézier operator direct and inverse theorems modulusof smoothness K-functional
分类号 O174.41 [理学—基础数学]
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参考文献9

  • 1Heilmann, M., Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. Theory Appl., 1989, 5(1): 105-127.
  • 2Bezier, P., Numerical Control---Mathematics and Applications, London: John Wiley \& Sons, 1972.
  • 3Chang G.Z., Generalized Bernstein-Bezier polynomials, J. Comput. Math., 1983, 1(4): 322-327.
  • 4Liu Z.X., Approximation of continuous functions by the generalized Bernstein-Bezier polynomials, Approx. Theory Appl., 1986, 2(4): 105-130.
  • 5Zeng X.M. and Gupta, V., Rate of convergence of Baskakov-Bezier type operators for locally bounded functions, Comput. Math. Appl., 2002, 44(1011): 1445-1453.
  • 6Zeng X.M. and Piriou, A., On the rate of convergence of two Bernstein-Bezier type operators for bounded variation functions, J. Approx. Theory, 1998, 95(3): 369-387.
  • 7Zeng X.M., On the rate of convergence of the generalized Szasz type operators for functions of bounded variation, J. Math. Anal. Appl., 1998, 226(2): 309-325.
  • 8Ditzian, Z. and Totik, V., Moduli of Smoothness, New York: Springer-Verlag, 1987.
  • 9Guo S.S., Qi Q.L. and Liu G.F., The central approximation theorems for Baskakov-Bezier operators, J. Approx. Theory, 2007, 147(1): 112-124.

同被引文献11

  • 1吴从忻 王廷辅.奥尔里奇空间及其应用[M].哈尔滨：黑龙江科学技术出版社,1983..
  • 2Voormolen MH, Mali WP, Lohle PN, et al. Percutaneous vertebroplasty compared with optimal pain medication treatment:short-tenn clinical outcome of patients with subacute or chronic painful osteoporotic vertebral compression fractures. The VERTOS study [ J ]. AJNR Am J Neuroradiol, 2007,28 ( 3 ) :555 - 560.
  • 3谢敦礼.连续正算子LM逼近的阶[J].杭州大学学报,1981,8(2):142-146.
  • 4Ditzian Z,Totik V.Moduli of Smoothness[M].New York:Springer-Verlag, 1987.
  • 5Wu Garidi.On Approximation by Polynomials in Orlicz Spaces [J].Approximation Theory and its Applications, 1991,7 (03):97-110.
  • 6Zeng X.M.and Gupta, [V].Rate of convergence Baskakov-Bezer type operators for locally bounded function, Comput, Math.Appl, 2002,44( 10/11 ) : 1445-1453.
  • 7谢敬礼.连续正算子岛逼近的阶[J].杭州大学学报,1981,(02):142-146.
  • 8Bezier P. Numerical Control-Mathematics and Applications[M]. London: John Wiley and Sons, 1972.
  • 9Wu Garidi. On Ap~ximation by Polynomials in Orlicz Spaces[J]. Approximation Theory and its Applications, 1991, 7 ( 3 ) 97-110.
  • 10Zeng X M, Gupta V. Rate of convergence Baskakov-Bezer type operators for locally bounded function[J]. Comput Math Appl, 2002, 44 ( 10/11 ): 1445-1453.

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数学进展
2013年 第3期

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