Shape preserving widths of Sobolev-type classes ofs-monotone functions on a finite interval

2003 ◽  
Vol 133 (1) ◽  
pp. 239-268 ◽  
Author(s):  
V. N. Konovalov ◽  
D. Leviatan
Keyword(s):  
Finite Interval ◽  
Sobolev Type ◽  
Monotone Functions ◽  
Shape Preserving ◽  
Type Classes

scholarly journals Widths and shape-preserving widths of Sobolev-type classes of s-monotone functions

2006 ◽  
Vol 140 (2) ◽  
pp. 101-126 ◽  
Author(s):  
J. Gilewicz ◽  
V.N. Konovalov ◽  
D. Leviatan
Keyword(s):  
Sobolev Type ◽  
Monotone Functions ◽  
Shape Preserving ◽  
Type Classes

Freeknot splines approximation of Sobolev-type classes of s-monotone functions

2007 ◽  
Vol 27 (2) ◽  
pp. 211-236 ◽  
Author(s):  
V. N. Konovalov ◽  
D. Leviatan
Keyword(s):  
Sobolev Type ◽  
Monotone Functions ◽  
Type Classes

scholarly journals Kolmogorov and Linear Widths of Weighted Sobolev-Type Classes on a Finite Interval, II

2001 ◽  
Vol 113 (2) ◽  
pp. 266-297 ◽  
Author(s):  
V.N Konovalov ◽  
D Leviatan
Keyword(s):  
Finite Interval ◽  
Sobolev Type ◽  
Type Classes

Kolmogorov, Linear and Pseudo-Dimensional Widths of Classes of s-Monotone Functions in 𝕃p, 0 < p < 1

2008 ◽  
Vol 51 (2) ◽  
pp. 236-248
Author(s):  
Victor N. Konovalov ◽  
Kirill A. Kopotun
Keyword(s):  
Unit Ball ◽  
Finite Interval ◽  
Divided Differences ◽  
Monotone Functions ◽  
Image Position

AbstractLet Bp be the unit ball in 𝕃p, 0 < p < 1, and let , s ∈ ℕ, be the set of all s-monotone functions on a finite interval I, i.e., consists of all functions x : I ⟼ ℝ such that the divided differences [x; t0, … , ts] of order s are nonnegative for all choices of (s + 1) distinct points t0, … , ts ∈ I. For the classes Bp := ∩ Bp, we obtain exact orders of Kolmogorov, linear and pseudo-dimensional widths in the spaces , 0 < q < p < 1:

Sobolev-type classes of functions with values in a metric space

1997 ◽  
Vol 38 (3) ◽  
pp. 567-583 ◽  
Author(s):  
Yu. G. Reshetnyak
Keyword(s):  
Metric Space ◽  
Sobolev Type ◽  
Type Classes

scholarly journals A Moment Problem for Discrete Nonpositive Measures on a Finite Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
M. U. Kalmykov ◽  
S. P. Sidorov
Keyword(s):  
Lower Bounds ◽  
Moment Problem ◽  
Finite Interval ◽  
Optimal Shape ◽  
Chebyshev System ◽  
Shape Preserving ◽  
Generalized Convex Functions ◽  
Moment Conditions ◽  
Shape Preserving Interpolation ◽  
Discrete Measures

We will estimate the upper and the lower bounds of the integral∫01Ω(t)dμ(t), whereμruns over all discrete measures, positive on some cones of generalized convex functions, and satisfying certain moment conditions with respect to a given Chebyshev system. Then we apply these estimations to find the error of optimal shape-preserving interpolation.

scholarly journals Approximation of Sobolev-Type Classes with Quasi-Seminorms

2005 ◽  
Vol 35 (2) ◽  
pp. 445-478 ◽  
Author(s):  
Z. Ditzian ◽  
V.N. Konovalov ◽  
D. Leviatan
Keyword(s):  
Sobolev Type ◽  
Type Classes
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