The polya-1 property for convex approximation |
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| Authors: | D A Legg D W Townsend |
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| Institution: | (1) Department of Mathematics, Indiana University-Purdue University at Fort Wayne, 46805 Fort Wayne, Indiana, USA |
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| Abstract: | If f∈Lp0, 1], let fp be its best Lp-approximant by convex functions. It is shown that if
![$$f \in \mathop \cup \limits_{p > 1} L_p 0,1], then \mathop {lim}\limits_{p \to 1} f_p (x)$$](/content/q785p76q2456v111/10496_2008_Article_BF02836304_TeX2GIFIE1.gif)
exists uniformly on closed subintervals of (0,1).
This research was partially supported by Grant No. 020-033-58 from the Faculty Research Committee, Idaho State University. |
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