Certain Szász-Mirakyan-beta operators
Springer Optimization and Its Applications, Springer International Publishing Ag, ss.363-386, 2014
- Yayın Türü: Kitapta Bölüm / Araştırma Kitabı
- Basım Tarihi: 2014
- Doi Numarası: 10.1007/978-3-319-06554-0__15
- Yayınevi: Springer International Publishing Ag
- Sayfa Sayıları: ss.363-386
- Anahtar Kelimeler: Confluent hypergeometric function, Direct estimates, Error estimations, Laguerre polynomials, Moments, Voronovskaja-type asymptotic formula
- Erciyes Üniversitesi Adresli: Evet
Özet
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.