✦ LIBER ✦

Approximation ofk-Monotone Functions

✍ Scribed by Kirill A. Kopotun

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 259 KB
Volume: 94
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1998.3189

No coin nor oath required. For personal study only.

✦ Synopsis

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 application, we prove a (positive) result on simultaneous approximation of a k-monotone function and its derivatives in L p , 0< p<1, metric, and also show that the rate of the best algebraic approximation of k-monotone functions (with bounded (k&2)nd derivatives in L p , 1< p< , is o(n &kÂ p ).

📜 SIMILAR VOLUMES

Best approximation by monotone functions

✍ P.W Smith; J.J Swetits 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 233 KB

Approximation of continuous and quasi-co

Approximation of continuous and quasi-continuous functions by monotone functions

✍ Richard B Darst; Salem Sahab 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 626 KB

Uniform approximation of completely mono

Uniform approximation of completely monotone functions by exponential sums

✍ Robert J McGlinn 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 382 KB

Uniform Estimates of Monotone and Convex

Uniform Estimates of Monotone and Convex Approximation of Smooth Functions

✍ K.A. Kopotun 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 852 KB

Efficient co-monotone approximation

✍ D.J. Newman 📂 Article 📅 1979 🏛 Elsevier Science 🌐 English ⚖ 154 KB

One Example in Monotone Approximation

✍ 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).