scholarly journals The Voronovskaja theorem for some linear positive operators defined by infinite sum

2011 ◽  
Vol 20 (1) ◽  
pp. 55-61
Author(s):  
DAN MICLAUS ◽  
◽  
OVIDIU T. POP ◽  
Keyword(s):  
Type Theorem ◽  
Positive Operators ◽  
Linear Positive Operators ◽  
Szász Operators ◽  
Voronovskaja Type Theorem ◽  
Infinite Sum

The main goal of this paper is to establish a Voronovskaja type theorem for the Szasz-Mirakjan-Schurer operators. As a particular case, we get also the Voronovskaja type theorem for the well known Mirakjan-Favard-Szasz operators.

scholarly journals About Some Linear Operators

2007 ◽  
Vol 2007 ◽  
pp. 1-13
Author(s):  
Ovidiu T. Pop
Keyword(s):  
Rate Of Convergence ◽  
General Class ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Positive Operators ◽  
Linear Operators ◽  
Linear Positive Operators ◽  
Voronovskaja Type Theorem

Using the method of Jakimovski and Leviatan from their work in 1969, we construct a general class of linear positive operators. We study the convergence, the evaluation for the rate of convergence in terms of the first modulus of smoothness and we give a Voronovskaja-type theorem for these operators.

scholarly journals A new modification of Durrmeyer type mixed hybrid operators

2018 ◽  
Vol 34 (1) ◽  
pp. 47-56
Author(s):  
ARUN KAJLA ◽  
◽  
TUNCER ACAR ◽  
Keyword(s):  
General Class ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Linear Positive Operators ◽  
Szász Operators ◽  
Voronovskaja Type Theorem ◽  
Integrable Functions ◽  
Durrmeyer Variant

In 2008 V. Mihes¸an constructed a general class of linear positive operators generalizing the Szasz operators. In ´ this article, a Durrmeyer variant of these operators is introduced which is a method to approximate the Lebesgue integrable functions. First, we derive some indispensable auxiliary results in the second section. We present a quantitative Voronovskaja type theorem, local approximation theorem by means of second order modulus of continuity and weighted approximation for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained.

scholarly journals The Voronovskaja type theorem for an extension of Szász-Mirakjan operators

2012 ◽  
Vol 45 (1) ◽  
Author(s):  
Ovidiu T. Pop ◽  
Dan Bărbosu ◽  
Dan Miclăuş
Keyword(s):  
Type Theorem ◽  
Positive Operators ◽  
Voronovskaja Type Theorem

AbstractRecently, C. Mortici defined a class of linear and positive operators depending on a certain function

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].

q-Szász operators which preserve x 2

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Nazim Mahmudov
Keyword(s):  
Global Convergence ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Test Function ◽  
The Third ◽  
Szász Operators ◽  
Voronovskaja Type Theorem

AbstractIn the present paper we construct q-Szász operators that preserve the third test function e 2. Rate of global convergence is obtained in the frame of weighted spaces. Furthermore, we obtain a Voronovskaja type theorem for these operators.

Statistical Korovkin-type theory for matrix-valued functions

2011 ◽  
Vol 48 (4) ◽  
pp. 489-508
Author(s):  
Oktay Duman ◽  
Esra Erkuş-Duman
Keyword(s):  
Type Theory ◽  
Statistical Convergence ◽  
Toeplitz Matrices ◽  
Type Theorem ◽  
Positive Operators ◽  
Korovkin Type Theorem ◽  
Linear Positive Operators ◽  
Numer Anal ◽  
Matrix Spaces

In this paper, using the notion of A-statistical convergence from the summability theory, we obtain a Korovkin-type theorem for the approximation by means of matrixvalued linear positive operators. We show that our theorem is more applicable than the result introduced by S. Serra-Capizzano [A Korovkin based approximation of multilevel Toeplitz matrices (with rectangular unstructured blocks) via multilevel trigonometric matrix spaces, SIAM J. Numer. Anal., 36 (1999), 1831–1857]. Furthermore, we compute the A-statistical rates of our approximation.

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