共查询到19条相似文献,搜索用时 140 毫秒
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正1引言记L_n(f,x)为Post-Widder算子■,其中■Post-Widder算子是Laplace变换的反演公式,有关Post-Widder算子的研究还比较少,该算子及其线性组合的逼近性质在L_p空间内得到了一些结果,如文献[1],[2],[3]等,但在Orlicz空间内Post-Widder算子的线性组合的逼近问题目前尚未见到有人研究,本文研究了算子L_n(f,x)在Orlicz空间内逼近的正定理,逆定理以及等价定理. 相似文献
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1引 言
1960年Meyer-K(o)nig W.和Zeller K.在[6]中提出了Meyer-K(o)nig-Zeller算子
Mn(f,x)=∞∑k=0f(k/(n+k))mn,k(x),0≤x<1,Mn(f,1):=f(1),mn,k(x)=(n+kk)xk(1-x)n+1,在[1,2,5,7,9,10,12]中对于此算子的逼近性质及各种修正了的Meyer-K(o)nig-Zeller算子作了研究,其中重要的变形是Kantorovich型的积分算子: M*n(f;x)=∞∑k=0((n+k)(n+k+1))/n∫(k+1)/(n+k+1)k/(n+k)f(u)dumn,k(x),x∈[0,),其中Mn(f,1):=f(1),mn,k(x)=(n+kk)xk(1+x)n+1,mn,-1(x):=0. V.Totik在[8]中给出了M*n(f;x)的Lp-逼近(1≤p<∞),王建力在[11]研究了其加权Lp-逼近(1≤p<∞).本文引进新的K+泛函,利用Ditzian-Totik模ω2ψ(f,t)研究了该算子的点态逼近性质,得到了它的逼近正、逆及等价定理. 相似文献
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给出并证明了Bernstein—Kantorovich算子逆中插式的B型强逆不等式,即存在l,使得ω_φ~(2r)(f,1/n~(1/2))≤C(||k_n~((2r-1))f-f||_∞+||K_(ln)~((2r-1))f-f||_∞). 相似文献
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陈志祥 《高校应用数学学报(A辑)》2008,23(1):79-85
讨论了一种神经网络算子f_n(x)=sum from -n~2 to n~2 (f(k/n))/(n~α)b(n~(1-α)(x-k/n)),对f(x)的逼近误差|f_n(x)-f(x)|的上界在f(x)为连续和N阶连续可导两种情形下分别给出了该网络算子逼近的Jackson型估计. 相似文献
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设S_n(f;x)表示如下的Sz(?)sz-Mirakjan算子:S_n(f;x)=sum from k=0 to ∞ f(k/n)S_(nk)(x),这里S_(nk)(x)=e~(-nx)(nx)~k/k!,x∈[0,∞),f∈C_[0,∞),C_[0,∞),表示在[0,∞)上连续且有界之函数集,1983年在[1]中给出了Sn(f;x)在一致逼近意义下的特征刻划,为讨论L_p逼近,[2]中引进了如下的Sz(?)sz-Mirakjan-Kantorovich算子: 相似文献
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关于Szász-Mirakjan型算子的加权逼近 总被引:2,自引:0,他引:2
设S_n(f;x)表示如下的Sz(?)sz-Mirakjan算子:S_n(f;x)=sum from k=0 to ∞ f(k/n)S_(nk)(x),这里S_(nk)(x)=e~(-nx)(nx)~k/k!,x∈[0,∞),f∈C_[0,∞),C_[0,∞),表示在[0,∞)上连续且有界之函数集,1983年在[1]中给出了Sn(f;x)在一致逼近意义下的特征刻划,为讨论L_p逼近,[2]中引进了如下的Sz(?)sz-Mirakjan-Kantorovich算子: 相似文献
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本文利用高阶光滑模ω■2r(f,t)p(1≤P≤∞)和ω■λ2r(f,t)∞(0≤λ≤1)得到了Szasz-Mirakian Kantorovich算子对于函数f∈Lp[0,00)(1≤P≤∞)的逼近等价定理. 相似文献
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Bernstein-Kantorovich quasi-interpolants K^(2r-1)n(f, x) are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ(f, t)p (1 ≤ p ≤+∞) are obtained. 相似文献
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DuanLiqin LiCuixiang 《分析论及其应用》2004,20(3):242-251
In this paper,we will use the 2r-th Ditzian-Totik modulus of smoothness wp^2r(f,t)p to discuss the direct and inverse theorem of approximation by Left-Bernstein-Durrmeyer quasi-interpolants Mn^[2r-1]f for functions of the space Lp[0,1](1≤p≤ ∞)。 相似文献
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The present paper first establishes a decomposition result for f(x)∈ C
r
C
r+1. By using this decomposition we thus can obtain an estimate of ∣f(x) - L
n
(f,x)∣ which reflects the influence of the position of the x's and ω(f
(r+1),δ)j, j = 0,1,...,s, on the error of approximation.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Constantin Costara 《Integral Equations and Operator Theory》2012,73(1):7-16
Let X be a complex Banach space and let B(X){\mathcal{B}(X)} be the space of all bounded linear operators on X. For x ? X{x \in X} and T ? B(X){T \in \mathcal{B}(X)}, let rT(x) = limsupn ? ¥ || Tnx|| 1/n{r_{T}(x) =\limsup_{n \rightarrow \infty} \| T^{n}x\| ^{1/n}} denote the local spectral radius of T at x. We prove that if j: B(X) ? B(X){\varphi : \mathcal{B}(X) \rightarrow \mathcal{B}(X)} is linear and surjective such that for every x ? X{x \in X} we have r
T
(x) = 0 if and only if rj(T)(x) = 0{r_{\varphi(T)}(x) = 0}, there exists then a nonzero complex number c such that j(T) = cT{\varphi(T) = cT} for all T ? B(X){T \in \mathcal{B}(X) }. We also prove that if Y is a complex Banach space and j:B(X) ? B(Y){\varphi :\mathcal{B}(X) \rightarrow \mathcal{B}(Y)} is linear and invertible for which there exists B ? B(Y, X){B \in \mathcal{B}(Y, X)} such that for y ? Y{y \in Y} we have r
T
(By) = 0 if and only if rj( T) (y)=0{ r_{\varphi ( T) }(y)=0}, then B is invertible and there exists a nonzero complex number c such that j(T) = cB-1TB{\varphi(T) =cB^{-1}TB} for all T ? B(X){T \in \mathcal{B}(X)}. 相似文献
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V. E. Maiorov 《Ukrainian Mathematical Journal》2010,62(3):452-466
We study the approximation of the classes of functions by the manifold R
n
formed by all possible linear combinations of n ridge functions of the form r(a · x)): It is proved that, for any 1 ≤ q ≤ p ≤ ∞, the deviation of the Sobolev class W
r
p
from the set R
n
of ridge functions in the space L
q
(B
d
) satisfies the sharp order n
-r/(d-1). 相似文献
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In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x) := (φ1(x), . . . , φr(x))T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x) := (φn1 ew(x), . . . , φrn ew(x))T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally,... 相似文献
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Florian Luca 《Monatshefte für Mathematik》2005,233(2):239-256
In [2], it was shown that if a and b are multiplicatively independent integers and ɛ > 0, then the inequality gcd (an − 1,bn − 1) < exp(ɛn) holds for all but finitely many positive integers n. Here, we generalize the above result. In particular, we show that if f(x),f1(x),g(x),g1(x) are non-zero polynomials with integer coefficients, then for every ɛ > 0, the inequality
gcd (f(n)an+g(n), f1(n)bn+g1(n)) < exp(ne){\rm gcd}\, (f(n)a^n+g(n), f_1(n)b^n+g_1(n)) < \exp(n\varepsilon)
holds for all but finitely many positive integers n. 相似文献
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We consider generalized potential operators with the kernel on bounded quasimetric measure space (X, μ, d) with doubling measure μ satisfying the upper growth condition μB(x, r) ? KrN, N ∈ (0, ∞). Under some natural assumptions on a(r) in terms of almost monotonicity we prove that such potential operators are bounded from the variable exponent Lebesgue space Lp(?)(X, μ) into a certain Musielak‐Orlicz space Lp(X, μ) with the N‐function Φ(x, r) defined by the exponent p(x) and the function a(r). A reformulation of the obtained result in terms of the Matuszewska‐Orlicz indices of the function a(r) is also given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
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Marie Madeleine Derriennic 《Journal of Approximation Theory》1981,31(4):325-343
We study here a new kind of modified Bernstein polynomial operators on L1(0, 1) introduced by J. L. Durrmeyer in [4]. We define for f integrable on [0, 1] the modified Bernstein polynomial Mn f: Mnf(x) = (n + 1) ∑nk = oPnk(x)∝10 Pnk(t) f(t) dt. If the derivative dr f/dxr with r 0 is continuous on [0, 1], dr/dxrMn f converge uniformly on [0,1] and supxε[0,1] ¦Mn f(x) − f(x)¦ 2ωf(1/trn) if ωf is the modulus of continuity of f. If f is in Sobolev space Wl,p(0, 1) with l 0, p 1, Mn f converge to f in wl,p(0, 1). 相似文献