Sidharth Manjari, Agrawal P N, Araci Serkan
Department of Mathematics, Indian Institute of Technology 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):122. doi: 10.1186/s13660-017-1396-x. Epub 2017 May 23.
The present paper introduces the Szász-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. Anal. 2012:680340, 2012). We establish the moments of the operator and a Voronvskaja type asymptotic theorem and then proceed to studying the convergence of the operators with the help of Lipschitz type space and weighted modulus of continuity. Next, we obtain a direct approximation theorem with the aid of unified Ditzian-Totik modulus of smoothness. Furthermore, we study the approximation of functions whose derivatives are locally of bounded variation.
本文介绍了基于博阿斯 - 巴克型多项式的萨兹 - 杜尔梅耶型算子，其中包括苏库等人（《抽象与应用分析》2012:680340，2012）所考虑的布伦克型多项式、谢弗多项式和Appell多项式。我们建立了该算子的矩和一个沃罗诺夫斯卡娅型渐近定理，然后借助利普希茨型空间和加权连续模来研究该算子的收敛性。接下来，我们借助统一的迪茨安 - 托蒂克光滑模得到一个直接逼近定理。此外，我们研究了其导数局部有界变差的函数的逼近问题。
