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The asymptotic property of approximation to \|x\| by Newman's rational operators

Authors:	TF Xie SP Zhou

Institution:	(1) Department of Mathematics, Lishui Teachers' College Lishui, Zhejiang, 323000, China;(2) Institute of Mathematics, Zhejiang Institute of Science and Technology Hangzhou, Zhejiang, 310018, China

Abstract:	Let $a = e^{ - 1/\sqrt n } ,p(x) = \Pi _{k = 1}^{n - 1} (a^k + x),r_n (x) = x\frac{{p(x) - p( - x)}} {{p(x) + p( - x)}}$ . The present note gives the asymptotoc formula of max $\mathop {\max }\limits_{\|x\| \leqq 1} \left\| {\|x\| - r_n (x)} \right\|$ . This revised version was published online in June 2006 with corrections to the Cover Date.

Keywords:	asymptotic property Newman's rational operator approximation
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