A test function theorem and apporoximation by pseudopolynomials

Badea, Cătălin; Badea, Ion; Gonska, Heiner

doi:10.1017/s0004972700004494

Cited by 56 publications

(32 citation statements)

References 4 publications

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“…Badea et al established the “test function theorem” for B‐continuous functions. Badea et al gave the quantitative estimate of the Korovkin‐type theorem in the Bögel space. Recently, several researchers contributed in this direction (cf other works, etc).…”

Section: Resultsmentioning

confidence: 99%

GBS operators of bivariate Bernstein‐Durrmeyer–type on a triangle

Ruchi

Baxhaku

Agrawal

2018

Math Methods in App Sciences

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The purpose of the present paper is to define the GBS (Generalized Boolean Sum) operators associated with the two‐dimensional Bernstein‐Durrmeyer operators introduced by Zhou 1992 and study its approximation properties. Furthermore, we show the convergence and comparison of convergence with the GBS of the Bernstein‐Kantorovich operators proposed by Deshwal et al 2017 by numerical examples and illustrations.

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Section: Resultsmentioning

confidence: 99%

GBS operators of bivariate Bernstein‐Durrmeyer–type on a triangle

Ruchi

Baxhaku

Agrawal

2018

Math Methods in App Sciences

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“…After this, Dobrescu and Matei [8] used the definitions of B-continuity and B-differentiability to obtain the approximating properties of GBS of bivariate Bernstein polynomials. In [3], Badea et al proved the "Test function theorem" for the functions defined in the Bögel space of continuous functions. In the same space the quantitative variant of a Korovkin-type theorem was given by Badea et al in [4].…”

Section: Construction Of Gbs Operators Of Chlodowsky-szász-appell Typementioning

confidence: 99%

Linking of Bernstein-Chlodowsky and Szász-Appell-Kantorovich type operators

Agrawal¹,

Kumar²,

Aracı³

2017

J. Nonlinear Sci. Appl.

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In the present paper, we define a sequence of bivariate operators by linking the Bernstein-Chlodowsky operators and the Szász-Kantorovich operators based on Appell polynomials. First, we establish the moments of the operators and then determine the rate of convergence of these operators in terms of the total and partial modulus of continuity. Next, we obtain the order of approximation of the considered operators in a weighted space. Furthermore, we define the associated GBS (Generalized Boolean Sum) operators of the linking operators and then study the rate of convergence with the aid of the Lipschitz class of Bögel continuous functions and the mixed modulus of smoothness.

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“…In approximation theory, the well-known Korovkin theorem is developed for B -continuous functions by Badea et al in [3,4]. In [3], the authors proved a Korovkin type theorem for approximation of B-continuous functions using the Boolean sum approach.…”

Section: Approximation In the Space Of Bögel Continuous Functionsmentioning

confidence: 99%

Degree of Approximation for Bivariate Chlodowsky–Szasz–Charlier Type Operators

Agrawal

İspir

2015

Results. Math.

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We consider a combination of Chlodowsky polynomials with generalized Szasz operators involving Charlier polynomials. We give the degree of approximation for these bivariate operators by means of the complete and partial modulus of continuity, and also by using weighted modulus of continuity. Furthermore, we construct a GBS (Generalized Boolean Sum) operator of bivariate Chlodowsky-Szasz-Charlier type and estimate the order of approximation in terms of mixed modulus of continuity.Mathematics Subject Classification. 41A25, 41A36, 41A63, 41A10.

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A test function theorem and apporoximation by pseudopolynomials

Abstract: W e prove a Korovkin-type theorem on approximation of bivariate functions in the space of B-continuous functions (introduced by K. Bogel in 1934). As consequences, some sequences of uniformly approximating pseudopolynomials are obtained.

Cited by 56 publications

References 4 publications

GBS operators of bivariate Bernstein‐Durrmeyer–type on a triangle

GBS operators of bivariate Bernstein‐Durrmeyer–type on a triangle

Linking of Bernstein-Chlodowsky and Szász-Appell-Kantorovich type operators

Degree of Approximation for Bivariate Chlodowsky–Szasz–Charlier Type Operators

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