The Research About Schurer Type Of Baskakov Operators' Approximation Property

Baskakov operators are regarded as an important tool on account of its favorable approximation properties mainly used to research the problem of operators' approximation.This paper mainly researches the approximation properties of certain generalized Schurer type Baskakov operators,q-Schurer-Baskakov-Szász–Beta operators,q-Schurer-Baskakov-Szász Stancu,bivariate q-Baskakov-Kantorovich operators and their deformation operators.The organization of this article is as follows:The first chapter,we introduce briefly the background and the progress on the operators approximation theory,then we generalize the overview of previous research progress of Schurer type operators,Baskakov operators,generalized Baskakov operators,q-Baskakov operators,bivariate Baskakov operators and their deformation operators both here and abroad.Finally,not only some definitions and related notations are described used in this article,but the main content of this article also included.The second chapter,we define a new class of Schurer-Baskakov-Szász–Beta operators based on q type through the knowledge of the K-functional and the modulus of smoothness' application so as to achieve the approximation order and some other conclusions.The third chapter,we consider the approximation properties of the Stancu type qSchurer-Baskakov-Szász–Beta operators on the basis of the second chapter,and obtain some approximation properties associated with the method of the K-functional and the modulus of smoothness.The fourth chapter,drawing the parameter ? into the generalized Baskakov operators,and integrating generalized deformation Schurer-Baskakov operators with Schurer-Baskakov-Stancu operators,we investigate the operators' recurrence relation for moment,convergence rate of weighted approximation and approximation order problems.The fifth chapter,we define the bivariate q-Kantorovich-Baskakov operators,and study it's center order of the moment and A-statistical convergence properties.We further prove its theorem concerning Korovkin and Voronovskaya.The sixth chapter,we summarize the whole article and look ahead Baskakov operators and their deformation operators as well as its combination operators approximation properties.