A Voronovskaya-type theorem for a certain nonlinear Bernstein operators
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Dosyalar
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Babes-Bolyai
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The present paper concerns with the nonlinear Bernstein operators NBnf of the form (NB(n)f)(x) = Sigma(n)(k=0) P-n,P-k (x, f (k/n)), 0 <= x <= 1, n is an element of N, acting on bounded functions on an interval [0, 1], where P-n,P-k satisfy some suitable assumptions. As a continuation of the very recent paper of the authors [11], we estimate the rate of convergence by modulus of continuity and provide a Voronovskaya-type formula for these operators. We note that our results are strict extensions of the classical ones, namely, the results dealing with the linear Bernstein polynomials.
Açıklama
Anahtar Kelimeler
Nonlinear Bernstein Operators, Modulus of Continuity, Moments, Voronovskaya-type Formula, (L-psi) Lipschitz Condition, Pointwise Convergence
Kaynak
Studia Universitatis Babes-Bolyai Mathematica
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
60
Sayı
2
