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Search: MSC category 41A25 ( Rate of convergence, degree of approximation )

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1. CMB Online first

Xu, Xu; Zhu, Laiyi
 Rational function operators from Poisson integrals In this paper, we construct two classes of rational function operators by using the Poisson integrals of the function on the whole real axis. The convergence rates of the uniform and mean approximation of such rational function operators on the whole real axis are studied. Keywords:rational function operators, Poisson integrals, convergence rate, uniform approximation, mean approximationCategories:41A20, 41A25, 41A35

2. CMB 2011 (vol 55 pp. 424)

Yang, Jianbin; Li, Song
 Convergence Rates of Cascade Algorithms with Infinitely Supported Masks We investigate the solutions of refinement equations of the form $$\phi(x)=\sum_{\alpha\in\mathbb Z^s}a(\alpha)\:\phi(Mx-\alpha),$$ where the function $\phi$ is in $L_p(\mathbb R^s)$$(1\le p\le\infty)$, $a$ is an infinitely supported sequence on $\mathbb Z^s$ called a refinement mask, and $M$ is an $s\times s$ integer matrix such that $\lim_{n\to\infty}M^{-n}=0$. Associated with the mask $a$ and $M$ is a linear operator $Q_{a,M}$ defined on $L_p(\mathbb R^s)$ by $Q_{a,M} \phi_0:=\sum_{\alpha\in\mathbb Z^s}a(\alpha)\phi_0(M\cdot-\alpha)$. Main results of this paper are related to the convergence rates of $(Q_{a,M}^n \phi_0)_{n=1,2,\dots}$ in $L_p(\mathbb R^s)$ with mask $a$ being infinitely supported. It is proved that under some appropriate conditions on the initial function $\phi_0$, $Q_{a,M}^n \phi_0$ converges in $L_p(\mathbb R^s)$ with an exponential rate. Keywords:refinement equations, infinitely supported mask, cascade algorithms, rates of convergenceCategories:39B12, 41A25, 42C40

3. CMB 2007 (vol 50 pp. 434)

Õzarslan, M. Ali; Duman, Oktay
 MKZ Type Operators Providing a Better Estimation on $[1/2,1)$ In the present paper, we introduce a modification of the Meyer-K\"{o}nig and Zeller (MKZ) operators which preserve the test functions $f_{0}(x)=1$ and $f_{2}(x)=x^{2}$, and we show that this modification provides a better estimation than the classical MKZ operators on the interval $[\frac{1}{2},1)$ with respect to the modulus of continuity and the Lipschitz class functionals. Furthermore, we present the $r-$th order generalization of our operators and study their approximation properties. Keywords:Meyer-KÃ¶nig and Zeller operators, Korovkin type approximation theorem, modulus of continuity, Lipschitz class functionalsCategories:41A25, 41A36
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