Approximation Of Linear Operators And Width Problems In Some Function Spaces

The studies on approximation of linear operators and widths theory are relatively perfect in continuity function spaces and L^p spaces. While in Orlicz spaces which are general spaces of L^p( p >1),the studies of these contents are slow. Therefore, in this paper, the approximation of linear operators are discussed in Orlicz spaces and Ba spaces which comprises a sequence of Orlicz spaces .The n-widths of some function classes are estimated in Orlicz spaces.This paper contains two chapters.Chapter one the theory on approximation of linear operators, the chapter which contains three sections mainly introduce the approximation of three difference types linear operators,and obtain corresponding approximation theory.Section one with the weighted modulus of smoothness as a tool, we prove the direct theorem of approximation by Stancu-kantorovich operators in Orlicz spaces.Section two with the weighted modulus of smoothness as a tool, we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in L_M^Ba spaces.Especially ,an approximation equivalent theorem of the operators is also obtained.Section three,in Orlicz spaces,the approximation degrees of Kantorovich-Vertesi rational interpolation operators are discussed,two kinds of estimation for degree of approximation are obtained.Chapter two problems of widths,the chapter contains four sections ,mainly study the widths estimate of some function classes.Section one ,in this section,we generalize the lower estimate on n-K width and n-G width of certain function classes defined by nonperiodic linear operators from L^P spaces to Orlicz spaces.Simultaneity, the corresponding dual cases are obtained.Section...