The Best Approximation Problems In Weighted H(?)lder Spaces

There are three chapters in this paper.We mainly discuss the approximation prob-lems of the functions approximated by polynomials in weighted unary and multivariate H(?)lder spaces.And we study the Jackson theorem and Bernstein theorem respectively,that is,direct theorem and inverse theorem of the best approximation.In the first part,we mainly study weighted unary H¨older spaces with weight x^?e^-x,and the best approx-imation properties and direct and inverse theorems of polynomials approximation are obtained.In the second part,we generalize the result of unary to multivariate weighted H(?)lder spaces with weight x^?y^?e^-x-yand obtain the corresponding direct theorem and inverse theorem.