On convergence of certain nonlinear Bernstein operators
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Dosyalar
Tarih
2016
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Nis, Fac Sci Math
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this article, we concern with the nonlinear Bernstein operators NBn f 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 [22], we estimate their pointwise convergence to a function f having derivatives of bounded (Jordan) variation on the interval [0, 1]. 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, Bounded Variation, (L - psi) Lipschitz Condition, Pointwise Convergence
Kaynak
Filomat
WoS Q Değeri
Q2
Scopus Q Değeri
Q3
Cilt
30
Sayı
1
