共查询到20条相似文献,搜索用时 15 毫秒
1.
G.A.Dzyubenko 《分析论及其应用》2017,33(1)
Suppose that a continuous 27r-periodic function f on the real axis changes its monotonicity at points y_1:-π≤ y_(2s)y_(2s-1)… y_1 π,s ∈ IN.In this PaPer,for each n≥N,a trigonometric polynomial P_n of order cn is found such that:P_n has the same monotonicity as f,everywhere except,perhaps,the small intervals(y_i-π/n,y_i+π/n)and‖f-P_n‖c(s)ω_3(f,π/n),where N is a constant depending only on mini=1,...,2s {y_i-y_(i+1)},c,c(s) are constants depending only on s,ω_3(f_1,·) is the modulus of smoothness of the 3-rd order of the function f,and ||·|| is the max-norm. 相似文献
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G. A. Dzyubenko 《分析论及其应用》2006,22(3):233-245
Let a function f ∈ C[-1, 1], changes its monotonisity at the finite collection Y := {y1,… ,ys} of s points yi ∈ (-1, 1). For each n ≥ N(Y), we construct an algebraic polynomial Pn, of degree ≤ n, which is comonotone with f, that is changes its monotonisity at the same points yi as f, and |f(x)-Pn(x)|≤c(s)ω2(f,(√1-x2)/n), x∈[-1,1],where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s and ω2 (f, t) is the second modulus of smoothness of f. 相似文献
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Jackson's Theorem on Bounded Symmetric Domains 总被引:1,自引:0,他引:1
Ming Zhi WANG Guang Bin REN 《数学学报(英文版)》2007,23(8):1391-1404
Polynomial approximation is studied on bounded symmetric domain Ω in C^n for holomorphic function spaces X such as Bloch-type spaces, Bergman-type spaces, Hardy spaces, Ω algebra and Lipschitz space. We extend the classical Jackson's theorem to several complex variables:Eκ(f,X)≤ω(1/k,f,X), where Eκ(f,X) is the deviation of the best approximation of f ∈X by polynomials of degree at most k with respect to the X-metric and ω(1/k,f,X) is the corresponding modulus of continuity. 相似文献
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Mathematical Notes - 相似文献
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All cases of the validity of the piecewise q-monotone analog of the Whitney inequality are clarified. For similar analogs of the Jackson inequality negative results are proved. 相似文献
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The main achievement of this paper is that we show, what was to us, a surprising conclusion, namely, twice continuously differentiable
functions in (0,1) (with some regular behavior at the endpoints) which change monotonicity at least once in the interval, are approximable
better by comonotone polynomials, than are such functions that are merely monotone. We obtain Jackson-type estimates for the
comonotone polynomial approximation of such functions that are impossible to achieve for monotone approximation.
July 7, 1998. Date revised: May 5, 1999. Date accepted: July 23, 1999. 相似文献
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The purpose of this article is to establish Jackson-type inequality in the polydiscs UN of for holomorphic spaces X, such as Bergman-type spaces, Hardy spaces, polydisc algebra and Lipschitz spaces. Namely,where is the deviation of the best approximation of fX by polynomials of degree at most kj about the jth variable zj with respect to the X-metric and is the corresponding modulus of continuity. 相似文献
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1 引言设f(x)∈C[-1,1]是分段单调函数,若要求逼近f(x)的多项式pn(x)也是分段单调的,且在每一分段上,f(x)与pn(x)具有相同的单调性,则称这种形式的逼近为共单调逼近,记En(f)=inf{‖f(x)-pn(x)‖|pn(x)∈πn,pn(x)在[-1,1]上与f(x)共单调},其 相似文献
10.
Z. Ditzian 《Proceedings of the American Mathematical Society》1996,124(6):1773-1781
We show that the -functional
where , is equivalent to the rate of convergence of a certain linear polynomial operator. This operator stems from a Riesz-type summability process of expansion by Legendre polynomials. We use the operator above to obtain a linear polynomial approximation operator with a rate comparable to that of the best polynomial approximation.
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Peeter Oja 《BIT Numerical Mathematics》2002,42(4):842-855
For any given data we propose the construction of an interpolating spline of class C
1, which is either a quadratic polynomial or a linear/linear rational function between the knots, and preserves the monotonicity of the data on the sections of rational intervals. We prove the uniqueness and existence of this spline. Numerical tests show good approximation properties and flexibility due to the non-coincidence of the given data arguments and the spline knots which can be chosen freely. 相似文献
13.
A. -R. K. Ramazanov 《Mathematical Notes》1996,60(5):536-543
For metrics of sign-sensitive weight, a generalization of the Jackson theorem and an analog of the Dolzhenko theorem on the estimate of the variation of a function in terms of its least rational deviations are obtained. In the same metric, two-sided estimates for rational deviations of the function signx are given.Translated fromMatematickeskie Zametki, Vol. 60, No. 5, pp. 715–725, November, 1996. 相似文献
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Pablo Martín Amelia García David J. Lpez 《Journal of Computational and Applied Mathematics》2001,130(1-2)
We approximate a function with periodic behaviour by means of a small modification of its Taylor polynomial. This modification is based on the work of Scheifele and will simplify the construction of special numerical methods for differential equations with near periodic solutions. 相似文献
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K. Kopotun D. Leviatan I. A. Shevchuk 《Proceedings of the American Mathematical Society》1999,127(2):409-415
Let change its convexity finitely many times in the interval, say times, at . We estimate the degree of approximation of by polynomials of degree , which change convexity exactly at the points . We show that provided is sufficiently large, depending on the location of the points , the rate of approximation is estimated by the third Ditzian-Totik modulus of smoothness of multiplied by a constant , which depends only on .
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Pointwise estimates are obtained for simultaneous approximation of a function f and its derivatives by means of an arbitrary sequence of bounded projection operators with some extra condition (1.3) (we do not require the operators to be linear) which map C[-1,1] into polynomials of degree n, augmented by the interpolation of f at some points near ±1. The present result essentially improved those in [BaKi3], and several applications are discussed in Section 4. 相似文献
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J. E. Brennan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(6):341-352
A solution is presented to the problem of uniform weighted polynomial approximation on bounded simply connected domains in the complex plane, that is analogous to Mergelyan’s solution to the classical Bernstein problem on the real line. 相似文献
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