Approximation by Reciprocals of Polynomials with Positive Coefficients in L
p
Spaces |
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| Authors: | Y Zhau SP Zhou |
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| Institution: | (1) The Mathematical Institute, Ningbo University, Ningbo, Zhejiang, 315211, China;(2) Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310028, China |
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| Abstract: | We prove that, if f(x)  L
p
0,1], 1 < p <  , f(x)  0, x 0,1], f  0, then there is a polynomial p(x)  +
n
such that  f - 1/p
LP
 C(p) (f,n
-1/2)
LP
where +
n
indicates the set of all polynomials of degree n with positive coeficients (see the definition (1) in the text). |
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| Keywords: | reciprocal Jackson type estimate nonnegative function L
p
space |
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