q-Bernstein-Kantorovich算子在紧圆盘的复逼近  

Approximation by a Complex-Bernstein-Kantorovich Operator in Compact Disks

作　　者：乌日汗[1] 韩领兄[1] Wurihan;HAN Lingxiong(College of Mathematics Science,Inner Mongolia Minzu University,Tongliao 028043,China)

机构地区：[1]内蒙古民族大学数学科学学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报(自然科学版)》2025年第2期92-96,共5页Journal of Inner Mongolia Minzu University:Natural Sciences Edition

基　　金：内蒙古自治区自然科学基金项目(2020LH01007)。

摘　　要：为了研究q-Bernstein-Kantorovich算子在复空间内对紧圆盘上解析函数的逼近性质,根据q-Bernstein-Kantorovich算子在实空间的定义,给出其在复空间的定义;在此基础上,利用q-Bernstein-Kantorovich算子的性质、复空间的相关性质和递推法、Bernstein不等式及高阶Cauchy积分公式等工具,参照几类q-算子在紧圆盘的复逼近问题的研究方法对q-Bernstein-Kantorovich算子进行了研究,得到q-Bernstein-Kantorovich算子在紧圆盘上同时逼近的一致逼近速度估计。In order to study the approximation properties to analytic functions of q-Bernstein-Kantorovich oper-ator in compact disks,according to the definition of q-Bernstein-Kantorovich operator in real space,its definition in complex space is given.On this basis,the properties of the q-Bernstein-Kantorovich operator,the correlation proper-ties of the complex space,recursive formula,the Bernstein inequality and the high order Cauchy integral formula are used to study the q-Bernstein-Kantorovich operator with reference to the method of several types of q-operators in the approximation properties of compact disks,the order of simultaneous approximation rate of the operator in com-pact disks is obtained.

关 键 词：复q-Bernstein-Kantorovich算子 紧圆盘 逼近估计 

分 类 号：O174.41[理学—数学]