Annals of Functional Analysis

Baskakov–Szász-type operators based on inverse Pólya–Eggenberger distribution

Arun Kajla, Ana Maria Acu, and P. N. Agrawal

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Abstract

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.

Article information

Source
Ann. Funct. Anal., Volume 8, Number 1 (2017), 106-123.

Dates
Received: 27 April 2016
Accepted: 1 July 2016
First available in Project Euclid: 31 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1477918638

Digital Object Identifier
doi:10.1215/20088752-3764507

Mathematical Reviews number (MathSciNet)
MR3566894

Zentralblatt MATH identifier
1354.41020

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
Secondary: 41A25: Rate of convergence, degree of approximation 41A28: Simultaneous approximation

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

Citation

Kajla, Arun; Acu, Ana Maria; Agrawal, P. N. Baskakov–Szász-type operators based on inverse Pólya–Eggenberger distribution. Ann. Funct. Anal. 8 (2017), no. 1, 106--123. doi:10.1215/20088752-3764507. https://projecteuclid.org/euclid.afa/1477918638


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