scholarly journals Shape-Preserving Widths of Weighted Sobolev-Type Classes of Positive, Monotone, and Convex Functions on a Finite Interval

2003 ◽  
Vol 19 (1) ◽  
pp. 23-58 ◽  
Author(s):  
Konovalov ◽  
Leviatan
Keyword(s):  
Convex Functions ◽  
Finite Interval ◽  
Sobolev Type ◽  
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

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

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

Some Extensions of a Theorem of Hardy, Littlewood and Pólya and Their Applications

1974 ◽  
Vol 26 (6) ◽  
pp. 1321-1340 ◽  
Author(s):  
Kong-Ming Chong
Keyword(s):  
Convex Functions ◽  
Finite Interval ◽  
Order Relation ◽  
Spectral Order ◽  
Measurable Functions ◽  
Approximation Lemma

In [6], by means of convex functions Φ :R→R, Hardy, Littlewood and Pólya proved a theorem characterizing the strong spectral order relation for any two measurable functions which are defined on a finite interval and which they implicitly assumed to be essentially bounded (cf. [6, the approximation lemma on p. 150 and Theorem 9 on p. 151 of their paper]; see also L. Mirsky [10, pp. 328-329] and H. D. Brunk [1,Theorem A, p. 820]).

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
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