Some Approximation Problems In Several Function Spaces

L~pspace has two kinds of generalization spaces :one is Ba space that is made up of a sequence of L~pspace ,and another is Orlicz space .With appearing of two kinds of spaces a ,we must think that some perfect results of L~pspace are carried out in two kinds of generalization spaces correspondingly. In this artical ,some approximation problems are studied in above two kinds of spaces .This artical is made up of three chapters.In chapter one, the problem of the order of convergence for the Fejer-Korovkin singular integral in Ba spaces is studied.Using the K-functional and modulus of smoothness,the upper and lower bounds of the rate of convergence are established.In chapter two, firstly,the problems of approximation for two kinds of rational interpolation operators in Orlicz spaces are studied ,and the Jackson type estimates of degree of approximation are obtained.After then,the problem of approximation by Linear combinations of Bernstein-Durrmeyer operators are studied.Chapter three consist of two parts.In first part,we studied the approximation by reciprocals of polynomials in Orlicz spaces and proved that if f ( x)∈L*M,change sign once in (-1,1),then there exists a rational function r ( x)∈Rn1 such thatIn second part, the Jackson type estimate of Muntz rational approximation in Orlicz spaces are studied Ler { } be a sequence of...