On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and t...

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Main Authors: Sezgin Sucu, Gürhan İçöz, Serhan Varma
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/680340
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spelling doaj-0621517389514e0db5c0499bc6a941942020-11-24T23:05:01ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/680340680340On Some Extensions of Szasz Operators Including Boas-Buck-Type PolynomialsSezgin Sucu0Gürhan İçöz1Serhan Varma2Department of Mathematics, Faculty of Science, Ankara University, Tandogan, 06100 Ankara, TurkeyDepartment of Mathematics, Faculty of Science, Gazi University, Teknikokullar, 06500 Ankara, TurkeyDepartment of Mathematics, Faculty of Science, Ankara University, Tandogan, 06100 Ankara, TurkeyThis paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.http://dx.doi.org/10.1155/2012/680340
collection DOAJ
language English
format Article
sources DOAJ
author Sezgin Sucu
Gürhan İçöz
Serhan Varma
spellingShingle Sezgin Sucu
Gürhan İçöz
Serhan Varma
On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials
Abstract and Applied Analysis
author_facet Sezgin Sucu
Gürhan İçöz
Serhan Varma
author_sort Sezgin Sucu
title On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials
title_short On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials
title_full On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials
title_fullStr On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials
title_full_unstemmed On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials
title_sort on some extensions of szasz operators including boas-buck-type polynomials
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.
url http://dx.doi.org/10.1155/2012/680340
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AT gurhanicoz onsomeextensionsofszaszoperatorsincludingboasbucktypepolynomials
AT serhanvarma onsomeextensionsofszaszoperatorsincludingboasbucktypepolynomials
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