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
β¦ LIBER β¦
Generalized monotone approximation inLpSpace
β Scribed by Yu Xiangming; Ma Yongpei
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 1989
- Tongue
- English
- Weight
- 344 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1439-7617
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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).