Certain Szász-Mirakyan-Beta Operators

N. K. Govil (), Vijay Gupta () and Danyal Soybaş ()
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N. K. Govil: Auburn University
Vijay Gupta: Netaji Subhas Institute of Technology
Danyal Soybaş: Faculty of Education Erciyes University Kayseri

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 363-386 from Springer

Abstract: Abstract In the present article we discuss direct estimates of the Durrmeyer type modifications of the well-known Szász-Mirakyan operators. The present article is divided into two sections. In the first section, we mention some of the different integral modifications of the Szász-Mirakyan operators and mention their direct results which were done in ordinary, and specially in the simultaneous approximation. In the second section for the Szász-Mirakyan-Beta operators, we find the alternate hypergeometric representation and propose their Stancu type generalization based on two parameters. We obtain the moments using confluent Hypergeometric functions. Also it is observed here that the moments are related to the Laguerre polynomials. We study direct approximation results for these Szász-Mirakyan-Beta-Stancu operators, which include a Voronovskaja-type asymptotic formula and error estimations in terms of modulus of continuity.

Keywords: Direct estimates; Confluent hypergeometric function; Laguerre polynomials; Moments; Voronovskaja-type asymptotic formula; Error estimations (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-06554-0_15

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DOI: 10.1007/978-3-319-06554-0_15

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