共查询到20条相似文献,搜索用时 156 毫秒
1.
In this study, motivating our earlier work [O. Duman and M.A. ?zarslan, Szász-Mirakjan type operators providing a better error
estimation. Appl. Math. Lett. 20, 1184–1188 (2007)], we investigate the local approximation properties of Szász-Mirakjan type operators. The second modulus
of smoothness and Petree’s K-functional are considered in proving our results.
Received: 17 September 2007 相似文献
2.
In 1985, Khan, R. A. established the asymptotic formulas of operators of probabilistic type inL1, space by introducing a newLp-norm. The purpose of this paper is to study the asymptotic rate of these operators, inLp (p>1) spaces.
Project supported by the National Natural Science Foundation of China 相似文献
3.
D. Souroujon 《Quaestiones Mathematicae》2019,42(3):289-296
In this paper we study the limit of the iterates of Jackson type operator. Our results continue the works of Badea [2] and Nagler et al. [9, 10]. The proofs are based on spectral theory of linear operators and are performed at first for Hilbert space and then are extended for some Banach spaces. 相似文献
4.
V. Totik 《Periodica Mathematica Hungarica》1985,16(2):115-126
It is proved that an integrable functionf can be approximated by the Kantorovich type modification of the Szász—Mirakjan and Baskakov operators inL
1 metric in the optimal order {n
–1} if and only if
2
f is of bounded variation where
and
, respectively. 相似文献
5.
The paper introduces Hermite-Fejér type (Hermite type) interpolation of higher order denoted by S
mn(f)(S*
mm(f)), and gives some basic properties including expression formulas, convergence relationship between S
mn(f) and H
mn(f) (Hermite-Fejér interpolation of higher order), and the saturation of S
mn(f).
Supported by the Science Foundation of Shanxi Province for Returned Scholars. 相似文献
6.
We study the approximation, Gelfand and Kolmogorov numbers of embeddings in function spaces of Besov and Triebel-Lizorkin type. Our aim here is to provide sharp estimates in several cases left open in the literature and give a complete overview of the known results. We also add some historical remarks. 相似文献
7.
8.
The purpose of the paper is to introduce Stancu‐type linear positive operators generated by Dunkl generalization of exponential function. We present approximation properties with the help of well‐known Korovkin‐type theorem and weighted Korovkin‐type theorem and also acquire the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K‐functional, and second‐order modulus of continuity by Dunkl analogue of Szász operators. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
9.
G. Oniani 《Georgian Mathematical Journal》1995,2(3):313-322
The process of Fejér type trigonometric convolution and its discrete analogue have equivalent uniform residues. The situation changes under pointwise comparison. In this direction negative results have been obtained by different authors. One result of such a type is given in the present paper. In particular, a counter-example is constructed for which both comparisons diverge on the set of complete measure. The smoothness of the counter-example as well as some other problems are investigated. 相似文献
10.
We present a simple change of basis technique for transforming one type of Pólya curve to another closely related Pólya curve form. Repeated use of this method yields algorithms for transforming one arbitrary Pólya form to another, as well as algorithms for evaluating, subdividing, and differentiating Pólya curves. These procedures can be applied to almost all Pólya curves, including Bézier curves and Lagrange interpolating polynomials. 相似文献
11.
In this paper we deal with shape preserving interpolation of data sets given on rectangular grids. The aim is to show that there exist spline interpolants of the continuity classC
2 which areS-convex, monotone, or positive if the data sets have these properties. This is done by using particular rational bicubic splines defined on the grids introduced by the data. Interpolants of the desired type can be constructed by a simple search procedure. 相似文献
12.
Annie Cuyt 《BIT Numerical Mathematics》1986,26(1):71-79
Several definitions of multivariate Padé approximants have been introduced during the last decade. We will here consider all types of definitions based on the choice that the coefficients in numerator and denominator of the multivariate Padé approximant are defined by means of a linear system of equations. In this case a determinant representation for the multivariate Padé approximant exists. We will show that a general recursive algorithm can be formulated to compute a multivariate Padé approximant given by any definition of this type. Here intermediate results in the recursive computation scheme will also be multivariate Padé approximants. Up to now such a recursive computation of multivariate Padé approximants only seemed possible in some special cases. 相似文献
13.
In the present paper we prove a Korovkin type approximation theorem for a sequence of positive linear operators acting from
a weighted space Cρ1 into a weighted space Bρ2 with the use of a matrix summability method which includes both convergence and almost convergence. We also study the rates
of convergence of these operators. 相似文献
14.
Lloyd N Trefethen 《Journal of Approximation Theory》1984,40(4):380-383
The method described by D. Braess (J. Approx. Theory40 (1984), 375–379) is applied to study approximation of ez on a disk rather than an interval. Let Emn be the distance in the supremum norm on ¦z¦ ? ? from ez to the set of rational functions of type (m, n). The analog of Braess' result turns out to be as m + n → ∞ This formula was obtained originally for a special case by E. Saff (J. Approx. Theory9 (1973), 97–101). 相似文献
15.
Let be a triangle in
and let
be the set of its three medians. We construct interpolants to smooth functions using transfinite (or blending) interpolation on
The interpolants are of type f(1)+g(2)+h(3), where (1,2,3) are the barycentric coordinates with respect to the vertices of . Based on an error representation formula, we prove that the interpolant is the unique best L1-approximant by functions of this type subject the function to be approximated is from a certain convexity cone in C3().Received: 17 December 2003 相似文献
16.
Shayne Waldron 《Numerische Mathematik》2000,85(3):469-484
Summary. Distribution theory is used to construct minimally supported Peano kernel type representations for linear functionals such as the error in multivariate Hermite interpolation. The simplest
case is that of representing the error in approximation to f by the constant polynomial f(a) in terms of integrals of the first order derivatives of f. This is discussed in detail. Here it is shown that suprisingly there exist many representations which are not minimally
supported, and involve the integration of first order derivatives over multidimensional regions. The distance of smooth functions
from the constants in the uniform norm is estimated using our representations for the error.
Received June 30, 1997 / Revised version received April 6, 1999 / Published online February 17, 2000 相似文献
17.
Ulrich Abel 《Journal of Approximation Theory》2004,126(2):115-125
The concern of this paper is the study of local approximation properties of the de la Vallée Poussin means Vn. We derive the complete asymptotic expansion of the operators Vn and their derivatives as n tends to infinity. It turns out that the appropriate representation is a series of reciprocal factorials. All coefficients are calculated explicitly. 相似文献
18.
In this paper we introduce and study a new sequence of positive linear operators acting on the space of Lebesgue-integrable
functions on the unit interval. These operators are defined by means of continuous selections of Borel measures and generalize
the Kantorovich operators. We investigate their approximation properties by presenting several estimates of the rate of convergence
by means of suitable moduli of smoothness. Some shape preserving properties are also shown.
Dedicated to the memory of Professor Aldo Cossu 相似文献
19.
U. Fidalgo Prieto 《Journal of Computational and Applied Mathematics》2010,233(6):1525-1533
Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field. 相似文献
20.
G. Mastroianni M. G. Russo W. Themistoclakis 《Integral Equations and Operator Theory》2002,42(1):57-89
The mapping properties of the Cauchy singular integral operator with constant coefficients are studied in couples of spaces equipped with weighted uniform norms. Recently weighted Besov type spaces got more and more interest in approximation theory and, in particular, in the numerical analysis of polynomial approximation methods for Cauchy singular integral equations on an interval. In a scale of pairs of weighted Besov spaces the authors state the boundedness and the invertibility of the Cauchy singular integral operator. Such result was not expected for a long time and it will affect further investigations essentially. The technique of the paper is based on properties of the de la Vallée Poussin operator constructed with respect to some Jacobi polynomials. 相似文献