scholarly journals Statistical approximation properties of λ-Bernstein operators based on q-integers

2019 ◽  
Vol 17 (1) ◽  
pp. 487-498 ◽  
Author(s):  
Qing-Bo Cai ◽  
Guorong Zhou ◽  
Junjie Li
Keyword(s):  
Error Bounds ◽  
Approximation Theorem ◽  
Absolute Error ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Central Moments ◽  
The Absolute

Abstract In this paper, we introduce a new generalization of λ-Bernstein operators based on q-integers, we obtain the moments and central moments of these operators, establish a statistical approximation theorem and give an example to show the convergence of these operators to f(x). It can be seen that in some cases the absolute error bounds are smaller than the case of classical q-Bernstein operators to f(x).

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.

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 Approximation properties of Kantorovich type q-Balázs-Szabados operators

2019 ◽  
Vol 52 (1) ◽  
pp. 10-19 ◽  
Author(s):  
Esma Yıldız Özkan
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Local Approximation ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Kantorovich Operators

AbstractIn this paper, we introduce a new kind of q-Balázs-Szabados-Kantorovich operators called q-BSK operators. We give a weighted statistical approximation theorem and the rate of convergence of the q-BSK operators. Also, we investigate the local approximation results. Further, we give some comparisons associated with the convergence of q-BSK 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 Integral modification of Apostol-Genocchi operators

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2533-2544
Author(s):  
N Neha ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Absolute Error ◽  
Local Approximation ◽  
Approximation Properties ◽  
Type Space ◽  
Durrmeyer Operators ◽  
Genocchi Polynomials ◽  
The Absolute ◽  
Mathematica Software

In this article, we consider Jain-Durrmeyer operators associated with the Apostol-Genocchi polynomials and study the approximation properties of these Durrmeyer operators. Furthermore, we examine the approximation behaviour of these operators including K-functional. We estimate the rate of convergence of the proposed operators for function in Lipschitz-type space and local approximation results by using modulus of continuity. Employing Mathematica software, to show the approximation and the absolute error graphically by varying the values of given parameters.

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.

scholarly journals On generalized Baskakov-Durrmeyer-Stancu type operators

2017 ◽  
Vol 50 (1) ◽  
pp. 144-155
Author(s):  
Angamuthu Sathish Kumar ◽  
Zoltán Finta ◽  
Purshottam Narain Agrawal
Keyword(s):  
Rate Of Convergence ◽  
Recurrence Relation ◽  
Approximation Property ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Modulus Of Smoothness ◽  
Direct Result ◽  
Approximation Properties ◽  
Statistical Approximation

Abstract In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

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