On convergence of certain nonlinear durrmeyer operators at lebesgue points
Küçük Resim Yok
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Singapore Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators ND(n)f of the form (ND(n)f)(x) = integral K-1(0)n (x,t, f (t))dt, 0 <= x <= 1, n is an element of N, acting on bounded functions on an interval [0, 1], where K-n (x, t, u) satisfies some suitable assumptions. Here we estimate the rate of convergence at a point x, which is a Lebesgue point of f is an element of L-1 ([0,1]) be such that psi(o) vertical bar f vertical bar is an element of BV ([0, 1]), where psi(o) vertical bar f vertical bar denotes the composition of the functions psi and vertical bar f vertical bar. The function psi : R-0(+) -> R-0(+) is continuous and concave with psi(0) = 0, psi(u) > 0 for u > 0, which appears from the (L - psi) Lipschitz conditions.
Açıklama
Anahtar Kelimeler
Nonlinear Durrmeyer Operators, Bounded Variation, Lipschitz Condition, Pointwise Convergence
Kaynak
Bulletin Of The Iranian Mathematical Society
WoS Q Değeri
Q4
Scopus Q Değeri
Q3
Cilt
41
Sayı
3
