Approximation Properties of a Certain Nonlinear Durrmeyer Operators

作者：Karsli Harun^*

来源：Filomat, 2017, 31(5): 1367-1380.

DOI：10.2298/FIL1705367K

• nonlinear Durrmeyer operators
• bounded variation
• (L-psi) Lipschitz condition
• pointwise convergence

The present paper is concerned with a certain sequence of the nonlinear Durrmeyer operators NDn, very recently introduced by the author [22] and [23], of the form (NDn f)(x) = integral(1)(0) K-n(x,t, f (t))dt, 0 <= x <= 1, n is an element of IN, acting on Lebesgue measurable functions defined on [0, 1]; where K-n (x, t, u) = F-n (x, t) H-n(u) satisfy some suitable assumptions. As a continuation of the very recent papers of the author [22] and [23], we estimate their pointwise convergence to functions f and psi o broken vertical bar f broken vertical bar having derivatives are of bounded (Jordan) variation on the interval [0, 1] .Here psi o broken vertical bar f broken vertical bar denotes the composition of the functions psi and broken vertical bar f broken vertical bar The function : R-0(+)-> R-0(+) is continuous and concave with psi(0) = 0, psi(u) > 0 for u > 0 : This study can be considered as an extension of the related results dealing with the classical Durrmeyer operators.

• 出版日期2017