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

• Mathematics • Previous Articles     Next Articles

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

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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