On Jackson Estimate for M\"{u}ntz Rational Approximation in $L^{p}_{[0,1]}$ Spaces
Received:March 04, 2005  Revised:October 25, 2005
Key Words: M\"{u}ntz rational functions   $L^p$ spaces   approximation rate.
Fund Project:the National Natural Science Foundation of China (10471130)
 Author Name Affiliation YU Dan-sheng Institute of Mathematics, Zhejiang Sci-Tech University, Zhejiang 310018, China ZHOU Song-ping Institute of Mathematics, Zhejiang Sci-Tech University, Zhejiang 310018, China
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Let $\Lambda=\{\lambda_{n}\}_{n=1}^{\infty}$ be a sequence of real numbers, and $\lambda_{n}\searrow 0$ as $n\rightarrow\infty$. Suppose that $\lambda_{n}\leq Mn^{-\frac{1}{2}}$ for $n=1,2, \cdots$, where $M>0$ is an absolute constant. The present paper considers the M\"{u}ntz rational approximation rate in $L_{[0,1]}^{p}$ spaces and gets $$R_{n} (f, \Lambda )_{L^{p}}\leq C_M \omega (f, n^{-\frac{1}{2}})_{L^{p}}$$ for $1 \leq p \leq \infty$.