On the Degre of L1-aproximation by Modified Bernstein Polynomials
Suresh Prasad Singh, O.P. Varshney, Govind Prasad (1983)
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Suresh Prasad Singh, O.P. Varshney, Govind Prasad (1983)
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Let || · || be the uniform norm in the unit disk. We study the quantities Mn (α) := inf (||zP(z) + α|| - α) where the infimum is taken over all polynomials P of degree n - 1 with ||P(z)|| = 1 and α > 0. In a recent paper by Fournier, Letac and Ruscheweyh (Math. Nachrichten 283 (2010), 193-199) it was shown that infα>0Mn (α) = 1/n. We find the exact values of Mn (α) and determine corresponding extremal polynomials. The method applied uses known cases of maximal ranges of polynomials. ...
Lupaş, Luciana (1998)
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Kim, Min-Soo, Kim, Taekyun, Lee, Byungje, Ryoo, Cheon-Seoung (2010)
Advances in Difference Equations [electronic only]
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