scholarly journals About the bivariate operators of Durrmeyer-type

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Ovidiu T. Pop ◽  
Mircea D. Fărcaş
Keyword(s):  
Approximation Properties ◽  
Gbs Operators ◽  
Bivariate Operators

AbstractThe aim of this paper is to study the convergence and approximation properties of the bivariate operators and GBS operators of Durrmeyer-type.

Bivariate q-Bernstein–Chlodowsky–Durrmeyer type operators and the associated GBS operators

2019 ◽  
Vol 13 (05) ◽  
pp. 2050091
Author(s):  
Tarul Garg ◽  
Nurhayat İspir ◽  
P. N. Agrawal
Keyword(s):  
Lipschitz Space ◽  
Continuous Functions ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Space Of Continuous Functions ◽  
Mixed Modulus Of Smoothness ◽  
Gbs Operators ◽  
Durrmeyer Type Operators ◽  
Mixed Modulus ◽  
Bivariate Operators

This paper deals with the approximation properties of the [Formula: see text]-bivariate Bernstein–Chlodowsky operators of Durrmeyer type. We investigate the approximation degree of the [Formula: see text]-bivariate operators for continuous functions in Lipschitz space and also with the help of partial modulus of continuity. Further, the Generalized Boolean Sum (GBS) operator of these bivariate [Formula: see text]–Bernstein–Chlodowsky–Durrmeyer operators is introduced and the rate of convergence in the Bögel space of continuous functions by means of the Lipschitz class and the mixed modulus of smoothness is examined. Furthermore, the convergence and its comparisons are shown by illustrative graphics for the [Formula: see text]-bivariate operators and the associated GBS operators to certain functions using Maple algorithms.

Some approximation properties by a class of bivariate operators

2019 ◽  
Vol 42 (16) ◽  
pp. 5551-5565 ◽  
Author(s):  
Ana Maria Acu ◽  
Tuncer Acar ◽  
Carmen‐Violeta Muraru ◽  
Voichiţa Adriana Radu
Keyword(s):  
Approximation Properties ◽  
Bivariate Operators

scholarly journals Bivariate α,q-Bernstein–Kantorovich Operators and GBS Operators of Bivariate α,q-Bernstein–Kantorovich Type

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1161 ◽  
Author(s):  
Qing-Bo Cai ◽  
Wen-Tao Cheng ◽  
Bayram Çekim
Keyword(s):  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Moduli Of Continuity ◽  
Mixed Modulus Of Smoothness ◽  
Differentiable Functions ◽  
Gbs Operators ◽  
Mixed Modulus ◽  
Bivariate Operators ◽  
Kantorovich Operators ◽  
Boolean Sum

In this paper, we introduce a family of bivariate α , q -Bernstein–Kantorovich operators and a family of G B S (Generalized Boolean Sum) operators of bivariate α , q -Bernstein–Kantorovich type. For the former, we obtain the estimate of moments and central moments, investigate the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and Peetre’s K-functional. For the latter, we estimate the rate of convergence of these G B S operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

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