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 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 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.

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 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 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 Some approximation results for (p,q)-Lupaş-Schurer operators

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 217-229 ◽  
Author(s):  
K. Kanat ◽  
M. Sofyalıoğlu
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation

In this paper, we introduce Lupa?-Schurer operators based on (p,q)-integers. Then, we deal with the approximation properties for (p,q)-Lupa?-Schurer operators based on Korovkin type approximation theorem. Moreover, we compute rate of convergence by using modulus of continuity, with the help of functions of Lipschitz class and Peetre?s K-functionals.

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.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

scholarly journals Approximation by Jakimovski-Leviatan-Stancu-Durrmeyer type operators

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1517-1530 ◽  
Author(s):  
M. Mursaleen ◽  
Shagufta Rahman ◽  
Khursheed Ansari
Keyword(s):  
Upper Bound ◽  
Simultaneous Approximation ◽  
Approximation Theorem ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators

In the present paper, we introduce Stancu type modification of Jakimovski-Leviatan-Durrmeyer operators. First, we estimate moments of these operators. Next, we study the problem of simultaneous approximation by these operators. An upper bound for the approximation to rth derivative of a function by these operators is established. Furthermore, we obtain A-statistical approximation properties of these operators with the help of universal korovkin type statistical approximation theorem.

scholarly journals On Some Statistical Approximation by (p,q)-Bleimann, Butzer and Hahn Operators

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 731 ◽  
Author(s):  
Khursheed Ansari ◽  
Ishfaq Ahmad ◽  
M. Mursaleen ◽  
Iqtadar Hussain
Keyword(s):  
Approximation Theorem ◽  
Rates Of Convergence ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Statistical Sense ◽  
Symmetric Property ◽  
Korovkin Approximation ◽  
Korovkin Approximation Theorem ◽  
Extra Parameter

In this article, we propose a different generalization of ( p , q ) -BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where ( p , q ) -integers contains symmetric property. We establish a Korovkin approximation theorem in the statistical sense and obtain the statistical rates of convergence. Furthermore, we also introduce a bivariate extension of proposed operators and carry many statistical approximation results. The extra parameter p plays an important role to symmetrize the q-BBH operators.

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