scholarly journals The (p; q)-Bernstein-Stancu operator of rough statistical convergence on triple sequence

2019 ◽  
Vol 38 (7) ◽  
pp. 125-136
Author(s):  
Ayhan Esi ◽  
M. Kemal Ozdemir ◽  
Nagarajan Subramanian
Keyword(s):  
Error Bound ◽  
Modulus Of Continuity ◽  
Statistical Convergence ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Stancu Operators

In the paper, we investigate rough statistical approximation properties of (p; q)-analogue of Bernstein-Stancu Operators. We study approximation properties based on rough statistical convergence. We also study error bound using modulus of continuity.

scholarly journals Statistical Approximation ofq-Bernstein-Schurer-Stancu-Kantorovich Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Qiu Lin
Keyword(s):  
Modulus Of Continuity ◽  
Statistical Convergence ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Stancu Operators ◽  
Kantorovich Operators

We introduce two kinds of Kantorovich-typeq-Bernstein-Schurer-Stancu operators. We first estimate moments ofq-Bernstein-Schurer-Stancu-Kantorovich operators. We also establish the statistical approximation properties of these operators. Furthermore, we study the rates of statistical convergence of these operators by means of modulus of continuity and the functions of Lipschitz class.

Statistical approximation properties of modified Durrmeyer q-Baskakov type operators with two parameters α and β

2016 ◽  
Vol 10 (02) ◽  
pp. 1750028
Author(s):  
Vishnu Narayan Mishra ◽  
Preeti Sharma
Keyword(s):  
Modulus Of Continuity ◽  
Maximal Function ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Rates Of Convergence ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Baskakov Operators ◽  
Two Parameters ◽  
Lipschitz Type Maximal Function

The main aim of this study is to obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established. Our results show that rates of convergence of our operators are at least as fast as classical Durrmeyer type modified Baskakov operators.

scholarly journals Statistical approximation properties of Stancu type q-Baskakov-Kantorovich operators

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1853-1868 ◽  
Author(s):  
Vishnu Mishra ◽  
Preeti Sharma ◽  
Adem Kiliçman ◽  
Dilip Jain
Keyword(s):  
Modulus Of Continuity ◽  
Statistical Convergence ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Type Function ◽  
Kantorovich Operators

In the present paper, we consider Stancu type generalization of Baskakov-Kantorovich operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type function are also established for said operators. Finally, we construct a bivariate generalization of the operator and also obtain the statistical approximation properties.

scholarly journals On the rates of convergence of the q-Lupaş-Stancu operators

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1151-1160
Author(s):  
Ogün Doğru ◽  
Gürhan İçoz ◽  
Kadir Kanat
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Rates Of Convergence ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Stancu Operators

We introduce a Stancu type generalization of the Lupa? operators based on the q-integers, rate of convergence of this modification are obtained by means of the modulus of continuity, Lipschitz class functions and Peetre?s K-functional. We will also introduce r-th order generalization of these operators and obtain its statistical approximation properties.

scholarly journals Approximation Properties of Bivariate Generalization of Meyer-König And Zeller Type Operators

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
H. Gül İnce ◽  
Esma Yildiz Özkan
Keyword(s):  
Modulus Of Continuity ◽  
Convergence Theorem ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
General Sequence ◽  
Bivariate Functions

Abstract In this paper, a bivariate generalization of a general sequence of Meyer-König and Zeller (MKZ) operators based on q-integers is constructed. Approximation properties of these operators are obtained by using either Korovkin-type statistical approximation theorem or Heping-type convergence theorem for bivariate functions. Rates of statistical convergence by means of modulus of continuity and the elements of Lipschitz class functionals are also established.

Statistical approximation by generalized Meyer-König and Zeller type operators

2003 ◽  
Vol 40 (3) ◽  
pp. 359-371 ◽  
Author(s):  
O. Doğru ◽  
O. Duman ◽  
C. Orhan
Keyword(s):  
Statistical Convergence ◽  
Approximation Properties ◽  
Statistical Approximation

In the present paper, we study a Kantorovich type generalization of Agratini's operators. Using A-statistical convergence, we will give the approximation properties of Agratini's operators and their Kantorovich type generalizations. We also give the rates of A-statistical convergence of these operators.

scholarly journals Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3473-3486 ◽  
Author(s):  
Faruk Özger
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Type Approximation ◽  
Bivariate Case ◽  
Estimate Rate ◽  
Kantorovich Operators

In this study, we consider statistical approximation properties of univariate and bivariate ?-Kantorovich operators. We estimate rate of weighted A-statistical convergence and prove a Voronovskajatype approximation theorem by a family of linear operators using the notion of weighted A-statistical convergence. We give some estimates for differences of ?-Bernstein and ?-Durrmeyer, and ?-Bernstein and ?-Kantorovich operators. We establish a Voronovskaja-type approximation theorem by weighted A-statistical convergence for the bivariate case.

scholarly journals Approximation properties of Jain-Stancu operators

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 1081-1088 ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Asymptotic Expansion ◽  
Error Estimation ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Linear Functions ◽  
Approximation Properties ◽  
Stancu Operators ◽  
Lagrange Expansion ◽  
Preserve Linear

In the present paper, we introduce the Stancu type Jain operators, which generalize the wellknown Sz?sz-Mirakyan operators via Lagrange expansion. We investigate their weighted approximation properties and compute the error of approximation by using the modulus of continuity. We also give an asymptotic expansion of Voronovskaya type. Finally, we introduce a modified form of our operators, which preserves linear functions, provides a better error estimation than the Jain operators and allows us to give global results in a certain subclass of C[0,?). Note that the usual Jain operators do not preserve linear functions and the global results in a certain subspace of C[0,?) can not be given for them.

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.

scholarly journals Approximation by Szász-Jakimovski-Leviatan-Type Operators via Aid of Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Present Article ◽  
Modulus Of Continuity ◽  
Statistical Convergence ◽  
Linear Operators ◽  
Approximation Properties ◽  
Appell Polynomials ◽  
Weighted Modulus Of Continuity ◽  
Dunkl Analogue ◽  
Weighted Modulus ◽  
Convergence Of Operators

The main purpose of the present article is to construct a newly Szász-Jakimovski-Leviatan-type positive linear operators in the Dunkl analogue by the aid of Appell polynomials. In order to investigate the approximation properties of these operators, first we estimate the moments and obtain the basic results. Further, we study the approximation by the use of modulus of continuity in the spaces of the Lipschitz functions, Peetres K-functional, and weighted modulus of continuity. Moreover, we study A-statistical convergence of operators and approximation properties of the bivariate case.

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