Acta Mathematica Hungarica
Volume/Issue:
Volume 111: Issue 4
Weighted approximation of functions by Szász--Mirakyan-type operators
Sz\'asz--Mirakyan operator, weighted modulus of smoothness, direct and converse results
Authors:
Biancamaria Della Vecchia Dipartimento di Matematica, Universitá di Roma ``La Sapienza'' Piazzale Aldo Moro 2, I-00185 Roma, Italy Piazzale Aldo Moro 2, I-00185 Roma, Italy

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Giuseppe Mastroianni Dipartimento di Matematica, Universitá della Basilicata Contrada Macchia Romana, I-85100 Potenza, Italy Contrada Macchia Romana, I-85100 Potenza, Italy

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Szabados J Alfréd Rényi Institute of Mathematics H-1364 Budapest, P.O.B. 127, Hungary H-1364 Budapest, P.O.B. 127, Hungary

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Pages:
325–345
Online Publication Date:
18 Jul 2006
Publication Date:
18 Jun 2006
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-006-0057-1
Keywords:
weighted modulus of smoothness; Szász--Mirakyan operator; direct and converse results
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Summary  

We give error estimates for the weighted approximation of functions with singularities at the endpoints on the semiaxis by some modifications of Sz\'asz--Mirakyan operators. To do so, we define a new weighted modulus of smoothness and prove its equivalence to the weighted K-functional. Also, the class of functions for which the modified Sz\'asz--Mirakyan operator can be defined will be extended to a much wider set than for the original operator.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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