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,?).

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.

scholarly journals Approximation by Parametric Extension of Szász-Mirakjan-Kantorovich Operators Involving the Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Rate Of Convergence ◽  
Weighted Space ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Appell Polynomials ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Dunkl Analogue ◽  
Kantorovich Operators

The purpose of this article is to introduce a Kantorovich variant of Szász-Mirakjan operators by including the Dunkl analogue involving the Appell polynomials, namely, the Szász-Mirakjan-Jakimovski-Leviatan-type positive linear operators. We study the global approximation in terms of uniform modulus of smoothness and calculate the local direct theorems of the rate of convergence with the help of Lipschitz-type maximal functions in weighted space. Furthermore, the Voronovskaja-type approximation theorems of this new operator are also presented.

scholarly journals Construction of Stancu-Type Bernstein Operators Based on Bézier Bases with Shape Parameter λ

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 316 ◽  
Author(s):  
Hari Srivastava ◽  
Faruk Özger ◽  
S. Mohiuddine
Keyword(s):  
Uniform Convergence ◽  
Shape Parameter ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Bernstein Operators ◽  
Global Approximation ◽  
Approximation Result ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Direct Approximation

We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ ∈ [ - 1 , 1 ] and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modulus of smoothness, calculate the rate of convergence via Lipschitz-type function, and discuss the Voronovskaja-type approximation theorems. Finally, in the last section, we construct the bivariate case of Stancu-type λ -Bernstein operators and study their approximation behaviors.

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.

scholarly journals Convergence properties of Ibragimov-Gadjiev-Durrmeyer operators

2015 ◽  
Vol 24 (1) ◽  
pp. 17-26
Author(s):  
EMRE DENIZ ◽  
◽  
ALI ARAL ◽  
Keyword(s):  
Weighted Space ◽  
Type Theorem ◽  
Approximation Error ◽  
Weighted Norm ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Korovkin Type Theorem ◽  
Durrmeyer Operators ◽  
Weighted Modulus ◽  
Direct Approximation

The purpose of the present paper is to study the local and global direct approximation properties of the Durrmeyer type generalization of Ibragimov Gadjiev operators defined in [Aral, A. and Acar, T., On Approximation Properties of Generalized Durrmeyer Operators, (submitted)]. The results obtained in this study consist of Korovkin type theorem which enables us to approximate a function uniformly by new Durrmeyer operators, and estimate for approximation error of the operators in terms of weighted modulus of continuity. These results are obtained for the functions which belong to weighted space with polynomial weighted norm by new operators which act on functions defined on the non compact interval [0.∞). We finally present a direct approximation result.

scholarly journals Direct and converse theorems for King operators

2020 ◽  
Vol 12 (1) ◽  
pp. 85-96
Author(s):  
Zoltán Finta
Keyword(s):  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
First Order ◽  
Converse Theorems ◽  
Direct Approximation

AbstractFor the sequence of King operators, we establish a direct approximation theorem via the first order Ditzian-Totik modulus of smoothness, and a converse approximation theorem of Berens-Lorentz-type.

scholarly journals Bézier variant of the Szász-Durrmeyer type operators based on the Poisson-Charlier polynomials

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3265-3273
Author(s):  
Arun Kajla ◽  
Dan Miclăuş
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Charlier Polynomials ◽  
Durrmeyer Type Operators ◽  
Direct Approximation ◽  
Bézier Variant

In the present paper we introduce the B?zier variant of the Sz?sz-Durrmeyer type operators, involving the Poisson-Charlier polynomials. Our study focuses on a direct approximation theorem in terms of the Ditzian-Totik modulus of smoothness and the rate of convergence for differential functions whose derivatives are of bounded variation.

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 Lp-Approximation (p≥1) by q-Kantorovich Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zoltán Finta
Keyword(s):  
Modulus Of Smoothness ◽  
Second Order ◽  
Approximation Theorems ◽  
Lp Approximation ◽  
Direct Approximation ◽  
Kantorovich Operators

For a new q-Kantorovich operator we establish direct approximation theorems in the space Lp[0,1],1≤p≤∞, via Ditzian-Totik modulus of smoothness of second order.

scholarly journals General family of exponential operators

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4043-4060
Author(s):  
Km. Lipi ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Error Estimation ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Approximation Of Functions ◽  
Direct Approximation ◽  
Derivatives Of

In this article, we deal with the approximation properties of Ismail-May operators [16] based on a non-negative real parameter ?. We provide some graphs and error estimation table for a numerical example depicting the convergence of our proposed operators. We further define the B?zier variant of these operators and give a direct approximation theorem using Ditizan-Totik modulus of smoothness and a Voronovoskaya type asymptotic theorem. We also study the error in approximation of functions having derivatives of bounded variation. Lastly, we introduce the bivariate generalization of Ismail May operators and estimate its rate of convergence for functions of Lipschitz class.

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