scholarly journals Kantorovich-Schurer bivariate operators

2004 ◽  
Vol 5 (2) ◽  
pp. 129 ◽  
Author(s):  
Dan Bărbosu
Keyword(s):  
Bivariate Operators

scholarly journals On the Voronovskaja-type formula for the Bleimann, Butzer and Hahn bivariate operators

2017 ◽  
Vol 33 (1) ◽  
pp. 35-42
Author(s):  
DAN BARBOSU ◽  
◽  
DAN MICLAUS ◽  
Keyword(s):  
Close Connection ◽  
Type Formula ◽  
Bivariate Operators

In this paper we present two new alternative ways for the proof of Voronovskaja-type formula of the Bleimann, Butzer and Hahn bivariate operators, using the close connection between the recalled operators and Bernstein bivariate operators, respectively Stancu bivariate operators.

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.

Bivariate Operators of Discrete and Integral Type

2018 ◽  
pp. 199-240
Author(s):  
Vijay Gupta ◽  
Themistocles M. Rassias ◽  
P. N. Agrawal ◽  
Ana Maria Acu
Keyword(s):  
Integral Type ◽  
Bivariate Operators

scholarly journals ABOUT THE BIVARIATE OPERATORS OF DURRMEYER-TYPE

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

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.

scholarly journals Better numerical approximation by λ-Durrmeyer-Bernstein type operators

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1405-1419
Author(s):  
Voichiţa Radu ◽  
Purshottam Agrawal ◽  
Jitendra Singh
Keyword(s):  
Numerical Approximation ◽  
Modulus Of Smoothness ◽  
Asymptotic Formulas ◽  
Bernstein Type ◽  
Mixed Modulus Of Smoothness ◽  
Differentiable Functions ◽  
Mixed Modulus ◽  
Bivariate Operators ◽  
Durrmeyer Variant ◽  
Theoretical Results

The main object of this paper is to construct a new Durrmeyer variant of the ?-Bernstein type operators which have better features than the classical one. Some results concerning the rate of convergence in terms of the first and second moduli of continuity and asymptotic formulas of these operators are given. Moreover, we define a bivariate case of these operators and investigate the approximation degree by means of the total and partial modulus of continuity and the Peetre?s K-functional. A Voronovskaja type asymptotic and Gr?ss-Voronovskaja theorem for the bivariate operators is also proven. Further, we introduce the associated GBS (Generalized Boolean Sum) operators and determine the order of convergence with the aid of the mixed modulus of smoothness for the B?gel continuous and B?gel differentiable functions. Finally the theoretical results are analyzed by numerical examples.

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