Some Approximation Problemes In L_M～(Ba) Spaces

The approximation theory of functions is one of the important branches of modern mathematics. It began in the 19 th century when two famous theorems were established. One says that the continuous functions can be approximated by certain polynomials which were established by Weierstrass in 1885 and the other that establishes characterization for approximation by polynomials was obtained by Chebyshev in 1859. It grew prosperous in 20th century and became an independent subject. People have generated a series of theories and methods in order to use the simple and computable functions to approximate general functions. For example, the best approximation, Fourier approximation, approximation by trigonometric polynomials, approximation by algebraic polynomials, linear operators approximation, interpolation approximation, rational approximation, approximation by reciprocals of polynomials, Müntz approximation and so on. This article studied linear operators approximation, interpolation approximation, approximation by reciprocals of polynomials, Müntz approximation in Ba spaces which were composed of a series of Orlicz spaces. This article contains five chapters.Chapter 1: In this section, we introduce the properties of the Orlicz spaces and the L_M^Ba spaces.Chapter 2: In this section, first we generalized the theorem in [4], [5] take advantage of theorem 1.2.1 , Hardy-Littlewood extremity functions and Steklov average function of order two, then we generalized the theorem in [6] by means of the weighted modulus of continuity of order...