Abstract and Applied Analysis

Approximation by the q -Szász-Mirakjan Operators

N. I. Mahmudov

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Abstract

This paper deals with approximating properties of the q-generalization of the Szász-Mirakjan operators in the case q > 1 . Quantitative estimates of the convergence in the polynomial-weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the q-Szász-Mirakjan operators ( q > 1 ) is of order q n versus 1/n for the classical Szász-Mirakjan operators.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 754217, 16 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475992

Digital Object Identifier
doi:10.1155/2012/754217

Mathematical Reviews number (MathSciNet)
MR3004883

Zentralblatt MATH identifier
1258.41010

Citation

Mahmudov, N. I. Approximation by the $q$ -Szász-Mirakjan Operators. Abstr. Appl. Anal. 2012 (2012), Article ID 754217, 16 pages. doi:10.1155/2012/754217. https://projecteuclid.org/euclid.aaa/1364475992


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