Note on a New Construction of Kantorovich Form q-Bernstein Operators Related to Shape Parameter λ  

作　　者：Qingbo Cai Resat Aslan 

机构地区：[1]Fujian Provincial Key Laboratory of Data-Intensive Computing,Key Laboratory of Intelligent Computing and Information Processing,School of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou,362000,China [2]Department of Mathematics,Faculty of Sciences and Arts,Harran University,Sanlıurfa,63300,Turkey

出　　处：《Computer Modeling in Engineering & Sciences》2022年第3期1479-1493,共15页工程与科学中的计算机建模（英文）

基　　金：This work is supported by the Natural Science Foundation of Fujian Province of China(Grant No.2020J01783);the Project for High-Level Talent Innovation and Entrepreneurship of Quanzhou(Grant No.2018C087R);the Program for New Century Excellent Talents in Fujian Province University.

摘　　要：The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to B′ezier basis functions with shape parameterλ∈[−1,1].Firstly,we compute some basic results such as moments and central moments,and derive the Korovkin type approximation theorem for these operators.Next,we estimate the order of convergence in terms of the usual modulus of continuity,for the functions belong to Lipschitz-type class and Peetre’s K-functional,respectively.Lastly,with the aid of Maple software,we present the comparison of the convergence of these newly defined operators to the certain function with some graphical illustrations and error estimation table.

关 键 词：Q-CALCULUS (λ q)-Bernstein polynomials order of convergence Lipschitz-type function Peetre’s K-functional 

分 类 号：O17[理学—数学]