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Monotone Iϕ-approximation

✍ Scribed by Miguel Marano; José María Quesada


Publisher
Springer
Year
1997
Tongue
English
Weight
283 KB
Volume
13
Category
Article
ISSN
1573-8175

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📜 SIMILAR VOLUMES


Structure of Best Radial Monotone Φ-Appr
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## Ž . convex function, ⌽ k 0, ⌽ 0 s 0. The ⌽-approximation of a real A A-measur-Ž< < . able function f is the process of minimizing H ⌽ f y h d among the real func-⍀ tions h of some class M M. In this paper we consider a class M M of ⌺-measurable functions, where ⌺ ; A A is a -lattice that is tot

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It is shown that an algebraic polynomial of degree k&1 which interpolates a k-monotone function f at k points, sufficiently approximates it, even if the points of interpolation are close to each other. It is well known that this result is not true in general for non-k-monotone functions. As an appli

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✍ I.A. Shevchuk 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 306 KB

For each non-negative integer n a function f=f n is constructed such that f has a continuous and non-negative derivative f $ on I :=[&1, 1] and where is the value of the best uniform approximation on I of the function f $ ( f ) by arbitrary (monotone on I ) algebraic polynomials of degree n (n+1).