scholarly journals Order of approximation for sampling Kantorovich operators

2014 ◽  
Vol 26 (3) ◽  
pp. 345-367 ◽  
Author(s):  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Order Of Approximation ◽  
Kantorovich Operators

scholarly journals Quantitative Estimates for Nonlinear Sampling Kantorovich Operators

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Nursel Çetin ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Orlicz Spaces ◽  
General Setting ◽  
Modulus Of Smoothness ◽  
Direct Approach ◽  
Order Of Approximation ◽  
Lipschitz Classes ◽  
General Frame ◽  
Quantitative Estimates ◽  
Nonlinear Sampling ◽  
Kantorovich Operators

AbstractIn this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of smoothness in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in $$L^{p}$$ L p -spaces, $$1\le p<\infty $$ 1 ≤ p < ∞ , and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming f in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improved in the $$L^p$$ L p -case, using a direct approach suitable to this context. At the end, we consider the particular cases of the nonlinear sampling Kantorovich operators constructed by using some special kernels.

scholarly journals Blending type Approximations by Kantorovich variant of α-Schurer operators

2021 ◽  
Author(s):  
Nadeem Rao ◽  
Pradeep Malik ◽  
Mamta Rani
Keyword(s):  
Numerical Analysis ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Weight Functions ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Global Approximation ◽  
Measurable Functions ◽  
Two Parameters ◽  
Kantorovich Operators

In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to approximate measurable functions on [0:1+q]; q > 0. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections . Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of rst and second order modulus of smoothness, Peetre’s K-functional and weight functions for these sequences in dierent spaces of functions.

scholarly journals An Inverse Result of Approximation by Sampling Kantorovich Series

2018 ◽  
Vol 62 (1) ◽  
pp. 265-280 ◽  
Author(s):  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Real Line ◽  
Representation Formula ◽  
Order Of Approximation ◽  
Generalized Sampling ◽  
Representation Formulas ◽  
Sampling Series ◽  
Bounded Functions ◽  
Saturation Theorem ◽  
Uniformly Continuous ◽  
Kantorovich Operators

AbstractIn the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, we prove that the best possible order of approximation that can be achieved by the above sampling series is the order one, otherwise the function being approximated turns out to be a constant. The above result is proved by exploiting a suitable representation formula which relates the sampling Kantorovich series with the well-known generalized sampling operators introduced by Butzer. At the end, some other applications of such representation formulas are presented, together with a discussion concerning the kernels of the above operators for which such an inverse result occurs.

scholarly journals Accurate Spectral Collocation Computations of High Order Eigenvalues for Singular Schrödinger Equations-Revisited

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 761
Author(s):  
Călin-Ioan Gheorghiu
Keyword(s):  
Schrödinger Equation ◽  
Small Parameter ◽  
Error Estimation ◽  
Schrodinger Equation ◽  
Error Control ◽  
High Order ◽  
Order Of Approximation ◽  
Schrödinger Equations ◽  
Spectral Collocation ◽  
Integration Interval

In this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We use the conventional ChC and SiC as well as Chebfun. In order to quantify the accuracy of our outcomes, we use the drift with respect to some parameters, i.e., the order of approximation N, the length of integration interval X, or a small parameter ε, of a set of eigenvalues of interest. The deficiency of orthogonality of eigenvectors, which approximate eigenfunctions, is also an indication of the accuracy of the computations. The drift of eigenvalues provides an error estimation and, from that, one can achieve an error control. In both situations, conventional spectral collocation or Chebfun, the computing codes are simple and very efficient. An example for each such code is displayed so that it can be used. An extension to a 2D problem is also considered.

scholarly journals On New Classes of Stancu-Kantorovich-Type Operators

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1235
Author(s):  
Bianca Ioana Vasian ◽  
Ștefan Lucian Garoiu ◽  
Cristina Maria Păcurar
Keyword(s):  
Test Functions ◽  
New Class ◽  
Convergence Results ◽  
Error Estimations ◽  
Kantorovich Operators

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

scholarly journals Shallow water waves in a rotating rectangular basin

2000 ◽  
Vol 24 (10) ◽  
pp. 649-661 ◽  
Author(s):  
Mohamed Atef Helal
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Equations Of Motion ◽  
System Of Nonlinear Equations ◽  
System Of Equations ◽  
Order Of Approximation ◽  
Shallow Water Waves ◽  
Nonlinear System Of Equations ◽  
Rectangular Basin ◽  
Shallow Water Approximation

This paper is mainly concerned with the motion of an incompressible fluid in a slowly rotating rectangular basin. The equations of motion of such a problem with its boundary conditions are reduced to a system of nonlinear equations, which is to be solved by applying the shallow water approximation theory. Each unknown of the problem is expanded asymptotically in terms of the small parameterϵwhich generally depends on some intrinsic quantities of the problem of study. For each order of approximation, the nonlinear system of equations is presented successively. It is worthy to note that such a study has useful applications in the oceanography.

scholarly journals On the order of approximation by Euler and Taylor means

1983 ◽  
Vol 39 (1) ◽  
pp. 24-38 ◽  
Author(s):  
C.K Chui ◽  
A.S.B Holland
Keyword(s):  
Order Of Approximation
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