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.

Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers

2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Nazim Mahmudov
Keyword(s):  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Weighted Modulus Of Smoothness ◽  
Weighted Modulus ◽  
Kantorovich Operators

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

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 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 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 Approximation by generalized Stancu type integral operators involving Sheffer polynomials

2018 ◽  
Vol 34 (2) ◽  
pp. 215-228
Author(s):  
M. MURSALEEN ◽  
◽  
SHAGUFTA RAHMAN ◽  
KHURSHEED J. ANSARI ◽  
◽  
...  
Keyword(s):  
Modulus Of Continuity ◽  
Integral Operators ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Weighted Modulus Of Continuity ◽  
Type Integral ◽  
Weighted Modulus ◽  
Sheffer Polynomials ◽  
Korovkin’S Theorem

In this article, we give a generalization of integral operators which involves Sheffer polynomials introduced by Sucu and Buy¨ ukyazici. We obtain approximation properties of our operators with the help of the univer- ¨ sal Korovkin’s theorem and study convergence properties by using modulus of continuity, the second order modulus of smoothness and Peetre’s K-functional. We have also established Voronovskaja type asymptotic formula. Furthermore, we study the convergence of these operators in weighted spaces of functions on the positive semi-axis and estimate the approximation by using weighted modulus of continuity.

scholarly journals Blending type Approximations by Kantorovich variant of α-Schurer operators

2021 ◽  
Author(s):  
Nadeem Rao ◽  
Pradeep Malik ◽  
Mamta Rani
Keyword(s):  
Numerical Analysis ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Weight Functions ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Global Approximation ◽  
Measurable Functions ◽  
Two Parameters ◽  
Kantorovich Operators

In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to approximate measurable functions on [0:1+q]; q > 0. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections . Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of rst and second order modulus of smoothness, Peetre’s K-functional and weight functions for these sequences in dierent spaces of functions.

scholarly journals New integral type operators

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2851-2865
Author(s):  
Emre Deniz ◽  
Ali Aral ◽  
Gulsum Ulusoy
Keyword(s):  
Pointwise Convergence ◽  
Weighted Space ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Integral Type ◽  
Type Estimate ◽  
Lp Space ◽  
Weighted Modulus ◽  
Direct Approximation ◽  
Kantorovich Operators

In this paper we construct new integral type operators including heritable properties of Baskakov Durrmeyer and Baskakov Kantorovich operators. Results concerning convergence of these operators in weighted space and the hypergeometric form of the operators are shown. Voronovskaya type estimate of the pointwise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, we give a direct approximation theorem for the operators in suitable weighted Lp space on [0,?).

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.

On the modification of the Szaśz–Durrmeyer operators

2016 ◽  
Vol 23 (3) ◽  
pp. 323-328 ◽  
Author(s):  
Ali Aral ◽  
Emre Deniz ◽  
Vijay Gupta
Keyword(s):  
Basis Function ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Quantitative Version ◽  
Durrmeyer Operators ◽  
Weighted Modulus Of Smoothness ◽  
Weighted Modulus ◽  
Direct Approximation

AbstractIn this paper we consider the modification of Szász–Durrmeyer operators based on the Jain basis function. Voronovskaya-type estimates of point-wise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, a direct approximation theorem for the operators is proved.

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