Results 1 to 10 of about 33 (33)
On the approximation by trigonometric polynomials in weighted Lorentz spaces
Journal of Function Spaces, Volume 8, Issue 1, Page 67-86, 2010., 2010 We obtain estimates of structural characteristics of 2π‐periodic functions by the best trigonometric approximations in weighted Lorentz spaces, and show that the order of generalized modulus of smoothness depends not only on the rate of the best approximation, but also on the metric of the spaces.
Vakhtang Kokilashvili +2 more
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Tight wavelet frames in Lebesgue and Sobolev spaces
Journal of Function Spaces, Volume 2, Issue 3, Page 227-252, 2004., 2004 We study tight wavelet frame systems in Lp(ℝd) and prove that such systems (under mild hypotheses) give atomic decompositions of Lp(ℝd) for 1≺p≺∞. We also characterize Lp(ℝd) and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for best m‐term approximation with the systems in Lp(ℝd) and prove that such ...
L. Borup +3 more
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Shape‐preserving multivariate polynomial approximation in C[−1,1]m
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 7, Page 325-333, 2004., 2004 We construct multivariate polynomials attached to a function f of m variables, m ≥ 2 , which approximate f with Jackson‐type rate involving a multivariate Ditzian‐Totik ω2φ‐modulus and preserve some natural kinds of multivariate monotonicity and convexity of function.
Ciprian S. Gal, Sorin G. Gal
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Some exact inequalities of Hardy‐Littlewood‐Polya type for periodic functions
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 47, Page 2517-2523, 2004., 2004 We investigate the following problem: for a given A ≥ 0, find the infimum of the set of B ≥ 0 such that the inequality ‖x(k)‖22≤A‖x(r)‖22+B‖x‖22, for k, r ∈ ℕ ∪ {0}, 0 ≤ k < r, holds for all sufficiently smooth functions.
Laith Emil Azar
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Infinite matrices, wavelet coefficients and frames
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 67, Page 3695-3702, 2004., 2004 We study the action of A on f ∈ L2(ℝ) and on its wavelet coefficients, where A=(almjk) lmjk is a double infinite matrix. We find the frame condition for A‐transform of f ∈ L2(ℝ) whose wavelet series expansion is known.
N. A. Sheikh, M. Mursaleen
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Rate of convergence on Baskakov‐Beta‐Bezier operators for bounded variation functions
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 8, Page 471-479, 2002., 2002 We introduce a new sequence of linear positive operators Bn,α(f, x), which is the Bezier variant of the well‐known Baskakov Beta operators and estimate the rate of convergence of Bn,α(f, x) for functions of bounded variation. We also propose an open problem for the readers.
Vijay Gupta
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Stečkin inequalities for summability methods
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 93-100, 1997., 1995 Stečkin proved an inequality on Fejér means of Fourier series He said, “Proving similar inequality for other summability method is an interesting problem.” We generalize Stečkin′s inequality and give various applications to summability methods.
Jia-Ding Cao
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A pointwise approximation theorem for linear combinations of Bernstein polynomials
Abstract and Applied Analysis, Volume 1, Issue 4, Page 397-406, 1996., 1996 Recently, Z. Ditzian gave an interesting direct estimate for Bernstein polynomials. In this paper we give direct and inverse results of this type for linear combinations of Bernstein polynomials.
Shunsheng Guo +4 more
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Properties of the modulus of continuity for monotonous convex functions and applications
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 3, Page 443-446, 1995., 1992 For a monotone convex function f ∈ C[a, b] we prove that the modulus of continuity w(f; h) is concave on [a, b] as function of h. Applications to approximation theory are obtained.
Sorin Gheorghe Gal
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Finite‐infinite range inequalities in the complex plane
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 4, Page 625-638, 1991., 1991 Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property. For any p, 0 < P ≤ ∞, there exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer n ≥ 1 and every
H. N. Mhaskar
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