科研之友
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摘要
Approximation to the function vertical bar x vertical bar plays an important role in approximation theory. This paper studies the approximation to the function x(alpha)sgn x, which equals vertical bar x vertical bar if alpha = 1. We construct a Newman Type Operator r(n)(x) and prove max(vertical bar x vertical bar <= 1) vertical bar x(alpha) sgn x - r(n)(x)vertical bar similar to Cn(1/4) e(-pi/2 root alpha n).
