scholarly journals On statistical approximation properties of Kantorovich type q-Bernstein operators

2010 ◽  
Vol 52 (5-6) ◽  
pp. 760-771 ◽  
Author(s):  
Özge Dalmanog˜lu ◽  
Ogün Dog˜ru
Keyword(s):  
Bernstein Operators ◽  
Approximation Properties ◽  
Statistical Approximation

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 q-Baskakov-Kantorovich operators

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Vijay Gupta ◽  
Cristina Radu
Keyword(s):  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Weighted Modulus Of Smoothness ◽  
Weighted Modulus ◽  
Kantorovich Operators

AbstractIn the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.

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