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February 2017 Baskakov–Szász-type operators based on inverse Pólya–Eggenberger distribution
Arun Kajla, Ana Maria Acu, P. N. Agrawal
Ann. Funct. Anal. 8(1): 106-123 (February 2017). DOI: 10.1215/20088752-3764507


The present article deals with the modified forms of the Baskakov and Szász basis functions. We introduce a Durrmeyer-type operator having the basis functions in summation and integration due to Stancu (1970) and Pǎltǎnea (2008). We obtain some approximation results, which include the Voronovskaja-type asymptotic formula, local approximation, error estimation in terms of the modulus of continuity, and weighted approximation. Also, the rate of convergence for functions with derivatives of bounded variation is established. Furthermore, the convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.


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Arun Kajla. Ana Maria Acu. P. N. Agrawal. "Baskakov–Szász-type operators based on inverse Pólya–Eggenberger distribution." Ann. Funct. Anal. 8 (1) 106 - 123, February 2017.


Received: 27 April 2016; Accepted: 1 July 2016; Published: February 2017
First available in Project Euclid: 31 October 2016

zbMATH: 1354.41020
MathSciNet: MR3566894
Digital Object Identifier: 10.1215/20088752-3764507

Primary: 26A15
Secondary: 41A25 , 41A28

Keywords: Baskakov operators , modulus of continuity , Pólya–Eggenberger distribution , Stancu operators , Szász operators

Rights: Copyright © 2017 Tusi Mathematical Research Group


Vol.8 • No. 1 • February 2017
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