scholarly journals Approximation properties of certain linear positive operators in polynomial weighted spaces of functions of one and two variables

2004 ◽  
pp. 51-64
Author(s):  
Zbigniew Walczak
Keyword(s):  
Positive Operators ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Linear Positive Operators

A class of linear positive operators in weighted spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Ayşegül Erençin ◽  
H. Gül İnce ◽  
Ali Olgun
Keyword(s):  
Differential Equation ◽  
Continuous Functions ◽  
Positive Operators ◽  
Weighted Spaces ◽  
Convergence Properties ◽  
Linear Positive Operators ◽  
Spaces Of Continuous Functions

AbstractIn this paper, we introduce a class of linear positive operators based on q-integers. For these operators we give some convergence properties in weighted spaces of continuous functions and present an application to differential equation related to q-derivatives. Furthermore, we give a Stancu-type remainder.

scholarly journals Approximation Properties of Certain Summation Integral Type Operators

2015 ◽  
Vol 48 (1) ◽  
Author(s):  
P. Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Positive Operators ◽  
Inverse Theorem ◽  
Approximation Properties ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Direct Results

AbstractIn the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

scholarly journals Bivariate Positive Operators in Polynomial Weighted Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Octavian Agratini
Keyword(s):  
Rate Of Convergence ◽  
Positive Operators ◽  
Weighted Spaces ◽  
Two Dimensional ◽  
Approximation Properties ◽  
Special Cases ◽  
Finite Sums

This paper aims to two-dimensional extension of some univariate positive approximation processes expressed by series. To be easier to use, we also modify this extension into finite sums. With respect to these two new classes designed, we investigate their approximation properties in polynomial weighted spaces. The rate of convergence is established, and special cases of our construction are highlighted.

King type generalization of Baskakov operators based on (𝑝, 𝑞) calculus with better approximation properties

Analysis ◽  
2020 ◽  
Vol 40 (4) ◽  
pp. 163-173
Author(s):  
Lakshmi Narayan Mishra ◽  
Shikha Pandey ◽  
Vishnu Narayan Mishra
Keyword(s):  
Modulus Of Continuity ◽  
Research Area ◽  
Positive Operators ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Type Result ◽  
Baskakov Operators ◽  
Linear Positive Operators ◽  
Test Function

AbstractApproximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p,q)-Baskakov operators, which reproduce the test function x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p,q)-Baskakov operators are explained and a Voronovskaja type result is obtained.

I-approximation properties of certain class of linear positive operators

2011 ◽  
Vol 48 (2) ◽  
pp. 205-219
Author(s):  
Nazim Mahmudov ◽  
Mehmet Özarslan ◽  
Pembe Sabancigil
Keyword(s):  
Modulus Of Smoothness ◽  
Positive Operators ◽  
Approximation Properties ◽  
Global Approximation ◽  
Linear Positive Operators ◽  
Durrmeyer Operators

In this paper we studyI-approximation properties of certain class of linear positive operators. The two main tools used in this paper areI-convergence and Ditzian-Totik modulus of smoothness. Furthermore, we defineq-Lupaş-Durrmeyer operators and give local and global approximation results for such operators.

q -Laguerre type linear positive operators

2007 ◽  
Vol 44 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
The Difference

The main object of this paper is to define the q -Laguerre type positive linear operators and investigate the approximation properties of these operators. The rate of convegence of these operators are studied by using the modulus of continuity, Peetre’s K -functional and Lipschitz class functional. The estimation to the difference | Mn +1, q ( ƒ ; χ )− Mn , q ( ƒ ; χ )| is also obtained for the Meyer-König and Zeller operators based on the q -integers [2]. Finally, the r -th order generalization of the q -Laguerre type operators are defined and their approximation properties and the rate of convergence of this r -th order generalization are also examined.

On positive operators involving a certain class of generating functions

2004 ◽  
Vol 41 (4) ◽  
pp. 415-429 ◽  
Author(s):  
O. Doğru ◽  
M. A. Özarslan ◽  
F. Taşdelen
Keyword(s):  
Differential Equations ◽  
Modulus Of Continuity ◽  
Generating Functions ◽  
Order Of Convergence ◽  
Positive Operators ◽  
Approximation Properties ◽  
Korovkin Theorem ◽  
Linear Positive Operators ◽  
General Sequence ◽  
The Korovkin Theorem

In this paper we introduced the general sequence of linear positive operators via generating functions. Approximation properties of these operators are obtained with the help of the Korovkin Theorem. The order of convergence of these operators computed by means of modulus of continuity Peetre’s K-furictiorial and the elements of the usual Lipschitz class. Also we introduce the r-th order generalization of these operators and we evaluate this generalization by the operators defined in this paper. Finally we give some applications to differential equations.

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