The new forms of Voronovskaya's theorem in weighted spaces
Yükleniyor...
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The Voronovskaya theorem which is one of the most important pointwise convergence results in the theory of approximation by linear positive operators (l.p.o) is considered in quantitative form. Most of the results presented in this paper mainly depend on the Taylor's formula for the functions belonging to weighted spaces. We first obtain an estimate for the remainder of Taylor's formula and by this estimate we give the Voronovskaya theorem in quantitative form for a class of sequences of l.p.o. The Gruss type approximation theorem and the Gruss-Voronovskaya-type theorem in quantitative form are obtained as well. We also give the Voronovskaya type results for the difference of l.p.o acting on weighted spaces. All results are also given for well-known operators, Szasz-Mirakyan and Baskakov operators as illustrative examples. Our results being Voronovskaya-type either describe the rate of pointwise convergence or present the error of approximation simultaneously.
Açıklama
Acar, Tuncer/0000-0003-0982-9459; Rasa, Ioan/0000-0002-5206-030X
Anahtar Kelimeler
Voronovskaya theorem, Gruss-type-Voronovskaya theorem, Weighted modulus of continuity, Difference of operators
Kaynak
Positivity
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
20
Sayı
1
Künye
closedAccess
