论文标题:q-算子的逼近问题
Two-flux Colliding Plane Waves in String Theory
论文作者 孟繁军
论文导师 汪和平,论文学位 硕士,论文专业 基础数学
论文单位 首都师范大学,点击次数 160,论文页数 29页File Size642k
2005-03-01论文网 http://www.lw23.com/lunwen_66019972/ q-Bernstein算子;q-Meyer-Konig and Zeller 算子;全整数;q-二项式系数;q-阶乘;连续模;一致收敛;收敛速度
q-Bernstein polynomials; q-Meyer Konig and Zeller operators; q-integers;q-factorial;q-binomial; convergence; modulas of smoothness; rate of approximation
本文主要研究q-Bernstein算子和q-Meyer K(?)nig and Zeller算子的逼近问题。 q-Bernstein算子是对经典的Bernstein算子的推广。1912年Bernstein用概率论方法给出了经典Bernstein算子,定义如下: B_nf(x):=sum from k=0 to n(f(k/n)(?)x~k(1-x)~(n-k)), n=1,2,…,其中f:[0,1]→R。 Bernstein多项式有许多杰出的性质,使它成为了研究的热门领域。特别是近些年来,开拓了新领域,出现了一些新的应用和推广。他的推广形式.即q-Bernstein多项式(或广义Bernstein多项式)为: Bn,q(f;x):=sum from k=0 to n(f([k]/[n])(?)x~k multiply from s=0 to (n-k-1)((1-q~sx)), 0≤x≤1。 当q=1时。q-Bernstein多项式与经典Bernstein多项式相同,当0This paper is concerned with the results of the approximation properties of the q-Bernstein polynomials B_(n,q) and q-Meyer Konig and Zeller operators M_(n,q) In 1912, using probability theory Bernstein defined polynomials called nowadays Bernstein Polynomials as follows: Let f : [0,1]→R, the Bernstein polynomial of / isLater it was found that Bernstein polynomials possess many remarkable properties, which made them an area of intensive research. Generalized Bernstein polynomials based on the 9-integers, or 9-Bernstein polynomials isIn the case 9 = 1, 9-Bernstein polynomials coincide with the classical ones. For 0 < q < 1, on the one hand, like the classical Bernstein polynomials, q-Bernstein polynomials share the good properties such as the shape preserving properties and monotonicity, on the other hand, the properties of 9-Bernstein polynomials differ essentially from those in classical case. For example, H.oruc and Neciber Tuncer ([8]) proved that for fixed 9, 0 < q < 1, B_(n,q)(f, x) converges uniformly to f(x) if and only if f is linear. Bernstein ([3]) proved that if f ∈ C[0,1], then the sequence B_nf(x) converges uniformly to f(x) on [0,1].In 2000, Tiberiu Trif ([12]) introduced the following generalization of Meyer Konig and Zeller operators, based on 9-integers. For each positive integer n, f∈ C[0,1], we defineIn this paper, we obtain a series of results as follows: where and the above estimate is sharp in the sense of order.(2) For any f∈ C[0,1], and for all x ∈ [0,1], q ∈ (0,1], M_(n,q)(f; x) converges uniformly (3) Let 0 < q < 1, f∈ C[0,1], thenwhere (4) For 0 < q ≤ r ≤ 1 and for f convex on [0,1], then M_(n.r) f≤ M_(n.q) f.
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