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.

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 A Spline Group – Korovkin Approximation Theorem

2015 ◽  
Vol 7 (2) ◽  
pp. 110
Author(s):  
Malik Saad Al-Muhja
Keyword(s):  
Linear Operator ◽  
Approximation Theorem ◽  
Positive Linear Operator ◽  
Homogeneous Groups ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Korovkin Approximation ◽  
Korovkin Approximation Theorem

In this paper, using homogeneous groups, we prove a Korovkin type approximation theorem for a spline groupby using the notion of a generalization of positive linear operator.

scholarly journals A Generalization of Lacunary Equistatistical Convergence of Positive Linear Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yusuf Kaya ◽  
Nazmiye Gönül
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Korovkin Approximation ◽  
Korovkin Approximation Theorem

In this paper we consider some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence. In particular we study lacunary equi-statistical convergence of approximating operators on spaces, the spaces of all real valued continuous functions de…ned on and satisfying some special conditions.

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 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 WeightedA-Statistical Convergence for Sequences of Positive Linear Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Abdullah Alotaibi ◽  
Bipan Hazarika
Keyword(s):  
Bernstein Polynomial ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Regular Matrix ◽  
Korovkin Approximation ◽  
Korovkin Approximation Theorem

We introduce the notion of weightedA-statistical convergence of a sequence, whereArepresents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weightedA-statistical convergence. Further, we give a rate of weightedA-statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our result.

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