Deshwal Sheetal, Agrawal P N, Araci Serkan
Indian Institute of Techology Roorkee, Roorkee, 247667 India.
Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep, 27410 Turkey.
J Inequal Appl. 2017;2017(1):57. doi: 10.1186/s13660-017-1328-9. Epub 2017 Mar 6.
In this paper, we construct a sequence of modified Stancu-Baskakov operators for a real valued function bounded on [Formula: see text], based on a function [Formula: see text]. This function [Formula: see text] is infinite times continuously differentiable on [Formula: see text] and satisfy the conditions [Formula: see text] and [Formula: see text] is bounded for all [Formula: see text]. We study the degree of approximation of these operators by means of the Peetre K-functional and the Ditzian-Totik modulus of smoothness. The quantitative Voronovskaja-type theorems are also established in terms of the first order Ditzian-Totik modulus of smoothness.
在本文中，基于一个函数(\varphi)，我们为在([a,b])上有界的实值函数构造了一列修正的斯坦库 - 巴斯卡科夫算子。这个函数(\varphi)在([a,b])上无限次连续可微，并且满足条件(\varphi^{(k)}(a)=\varphi^{(k)}(b)=0)（(k = 0,1,2,\cdots)），且对于所有(x\in[a,b])，(\varphi(x))是有界的。我们借助皮特雷(K) - 泛函和迪茨安 - 托蒂克光滑模来研究这些算子的逼近程度。还根据一阶迪茨安 - 托蒂克光滑模建立了定量的沃罗诺夫斯卡娅型定理。
