scholarly journals The generalization of some results for Bernstein and Stancu operators

2011 ◽  
Vol 20 (2) ◽  
pp. 147-156
Author(s):  
DAN MICLAUS ◽  
◽  
PETRU I. BRAICA ◽  
Keyword(s):  
Uniform Convergence ◽  
Type Theorem ◽  
Bernstein Operators ◽  
Order Of Approximation ◽  
Test Functions ◽  
Stancu Operators ◽  
Voronovskaja Type Theorem

In the present paper we generalize some results for Bernstein and Stancu operators. Firstly, we establish a relationship between two results concerning calculation of test functions by Bernstein operators. Secondly, using this relationship and some known results we prove in every case a Voronovskaja type theorem, the uniform convergence and the order of approximation for Bernstein and Stancu operators.

scholarly journals The generalization of certain results for Szasz-Mirakjan-Schurer operators

2012 ◽  
Vol 21 (1) ◽  
pp. 79-85
Author(s):  
DAN MICLAUS ◽  
◽  
OVIDIU T. POP ◽  
Keyword(s):  
Uniform Convergence ◽  
Present Article ◽  
General Formula ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Order Of Approximation ◽  
Test Functions ◽  
Voronovskaja Type Theorem

The present article continues earlier research by authors, in order to reach two goals. Firstly, we give a general formula concerning calculation of the test functions by Szasz-Mirakjan-Schurer operators and secondly, we establish a Voronovskaja type theorem, the uniform convergence and the ´ order of approximation using the modulus of continuity for the same operators.

Bernstein-type operators which preserve exactly two test functions

2013 ◽  
Vol 50 (4) ◽  
pp. 393-405 ◽  
Author(s):  
Ovidiu Pop ◽  
Dan Bǎrbosu ◽  
Petru Braica
Keyword(s):  
Convergence Theorem ◽  
General Class ◽  
Type Theorem ◽  
Positive Operators ◽  
Bernstein Operators ◽  
Test Functions ◽  
Approximation Properties ◽  
Bernstein Type ◽  
Voronovskaja Type Theorem

A general class of linear and positive operators dened by nite sum is constructed. Some of their approximation properties, including a convergence theorem and a Voronovskaja-type theorem are established. Next, the operators of the considered class which preserve exactly two test functions from the set {e0, e1, e2} are determined. It is proved that the test functions e0 and e1 are preserved only by the Bernstein operators, the test functions e0 and e2 only by the King operators while the test functions e1 and e2 only by the operators recently introduced by P. I. Braica, O. T. Pop and A. D. Indrea in [4].

scholarly journals Note on a Schurer-Stancu-type operator

2015 ◽  
Vol 24 (1) ◽  
pp. 61-67
Author(s):  
ADRIAN D. INDREA ◽  
◽  
ANAMARIA INDREA ◽  
PETRU I. BRAICA ◽  
◽  
...  
Keyword(s):  
Type Theorem ◽  
Type Operator ◽  
Test Functions ◽  
New Class ◽  
Voronovskaja Type Theorem

The aim of this paper is to introduce a class of operators of Schurer-Stancu-type with the property that the test functions e0 and e1 are reproduced. Also, in our approach, a theorem of error approximation and a Voronovskaja-type theorem for this operators are obtained. Finally, we study the convergence of the iterates for our new class of operators.

scholarly journals Approximation properties of mixed sampling-Kantorovich operators

2020 ◽  
Vol 115 (1) ◽  
Author(s):  
Laura Angeloni ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Uniform Convergence ◽  
Type Theorem ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem ◽  
Quantitative Estimates ◽  
Kantorovich Operators

Abstract In the present paper we study the pointwise and uniform convergence properties of a family of multidimensional sampling Kantorovich type operators. Moreover, besides convergence, quantitative estimates and a Voronovskaja type theorem have been established.

scholarly journals Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
S. A. Mohiuddine
Keyword(s):  
Rate Of Convergence ◽  
Differentiable Function ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Order Of Approximation ◽  
Mixed Modulus Of Smoothness ◽  
Voronovskaja Type Theorem ◽  
Gbs Operators ◽  
Mixed Modulus ◽  
Boolean Sum

AbstractWe construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K-functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.

scholarly journals Generalized p,q-Gamma-type operators

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wen-Tao Cheng ◽  
Qing-Bo Cai
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

In the present paper, the generalized p,q-gamma-type operators based on p,q-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. Also, the rate of convergence, weighted approximation, and pointwise estimates of these operators are studied. Finally, a Voronovskaja-type theorem is presented.

Modified Lupaş-Jain operators

2020 ◽  
Vol 70 (2) ◽  
pp. 431-440 ◽  
Author(s):  
Murat Bodur
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Order Of Approximation ◽  
Weighted Modulus Of Continuity ◽  
Quantitative Form ◽  
Voronovskaya Type Theorem ◽  
Weighted Modulus

Abstract The goal of this paper is to propose a modification of Lupaş-Jain operators based on a function ρ having some properties. Primarily, the convergence of given operators in weighted spaces is discussed. Then, order of approximation via weighted modulus of continuity is computed for these operators. Further, Voronovskaya type theorem in quantitative form is taken into consideration, as well. Ultimately, some graphical results that illustrate the convergence of investigated operators to f are given.

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