The direct and converse theorems for best approximation of trigonometric polynomial in Lp,α (X)

The purpose of this paper is studying best approximation of unbounded functions by suitable trigonometric polynomials of one variable in Lp,α (X) , where has been introduce of the direct and inverse theorems of approximation and prove the criteria of the precise order of decrease of the best approximation in these spaces. Moreover, we obtain strong converse inequalities for some methods of approximation of functions. We obtain the relationship between of K-functional and modulus of smoothness.