Weighted Approximation Properties Of Modified Baskakov Type Operators Property

Function approximation theory is now an important branch of mathematics,its main content is to use some simple functions to approximate complex functions.Function approximation theory got to flourish,under Bernstein,Jackson and many other outstanding scientists actively participate in and drive within,making the approximation theory to become an independent discipline and gradually to perfect.The approximation of operator is an important part of function approximation theory,and the main research question is the approximation problem about linear operator sequence.This paper mainly studies the modified Baskakov operators,investigating the weighted approximation properties of a new class of modified Baskakov type operators and their linear combination operators,On the basis of relevant theories.This text is divided into the following chapters:The chapter 1 is the introduction of the article.Firstly,we review the historical background and development status of function approximation theory briefly.Secondly,we summarize some of the research results about the Baskakov type operators at home and abroad.Finally,we introduced some basic definitions and related symbols that we will use.In the chapter 2,we mainly investigate strong converse inequality weighted approximation problem by a new kind of Baskakov type operators.Mainly using K-functional combine with modulus of smoothness is discussed with weighted approximation problem about the singularity function by the modified Baskakov operators,obtaining the Stechkin-Marchaud type inequality that pointwise weighted approximation inverse theorems.In the chapter 3,we study a new kind of a linear combination of Baskakov Operators which be constructed on the endpoint by Lagrange interpolation function instead of the value method.We obtain the corresponding direct and inverse theorem of weighted approximation about the functions which has singularities in the endpoint using this type of operators.In the chapter 4,we study the weighted approximation problem of higher order derivatives of a class of modified Baskakov operators,and establish the pointwise theorems.The operators are the same as those in the third chapter.In the chapter 5,we make a summary of the whole paper firstly,then we make a prospect for weighted approximation problem by the Baskakov operators and its deformation operators about the singularity function.