journal6 ›› 2003, Vol. 24 ›› Issue (2): 47-51.

• 数学 • 上一篇    下一篇

一类新算子的同时逼近

  

  1. (宁夏大学数学与电算工程系,宁夏 银川750021)
  • 出版日期:2003-06-15 发布日期:2012-11-07
  • 作者简介:王丽(1977-),女,宁夏银川人,宁夏大学数学与电算工程系硕士研究生,主要从事函数逼近论研究.
  • 基金资助:

    宁夏自然科学基金资助项目(A001);宁夏大学科学研究基金资助项目(002102)

Simultaneous Approximation by a New Class of Operators

  1. (Department of Mathematics and Electronic Computing Engineering,Ningxia Unversity,Yinchuan 750021,Ningxia China)
  • Online:2003-06-15 Published:2012-11-07

摘要:引入一种新的正线性算子并研究它对于无界函数的同时逼近.设f∈Cβ[0,∞),r∈N,f(x)在[0,∞)存在r阶导数,则limn∞M(r)n,α(f(t),x)=f(r)(x);若f(r)(x)∈C(a-η,b+η)(η>0),则M(r)n,α(f,x)f(r)(x)在x∈[a,b]一致成立.设f∈Cβ[0,∞),f(x)在[0,∞)上存在r+2阶导数,则limn∞n[M(r)n,α(f,x)-f(r)(x)]=α[r(r+1)f(r)(x)+(2(r+1)x+r)f(r+1)(x)+x(1+x)f(r+2)(x)];若f(r+2)(x)∈Ca-η,b+η)(η>0),则上式在[a,b]一致成立.

关键词: 同时逼近, 光滑模, 渐进展开, 逼近度

Abstract: A new class of positive linear operators is introduced,and the simultaneous approximation of unbounded functions is studied.Let f∈Cβ[0,∞),r∈N,derivative of ordern n exists in f(x) in [0,∞),then limn∞M(r)n,α(f(t),x)=f(r)(x),if f(r)(x)∈C(a-η,b+η)(η>0),then M(r)n,α(f,x)f(r)(x) is applicable when x∈[a,b].If f∈Cβ[0,∞),f(x) has derivative of order r+2 in [0,∞),then limn∞n[M(r)n,α(f,x)-f(r)(x)]=α[r(r+1)f(r)(x)+(2(r+1)x+r)f(r+1)(x)+x(1+x)f(r+2)(x)],if f(r+2)(x)∈Ca-η,b+η)(η>0),then the above equation is valid in [a,b].

Key words: simultaneous approximation, modulus of smoothness, asymptotic expansion ;approximation degree

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