A Study on the Approximations of Bounded Functions in the Locally Global Spaces (L_δ,P), (0 < P ≤ 1)

The purpose of the present paper is to evaluate the error of the approximation of the function F defined in [0,1] by Bernstein polynomial in L_P space (0 < P ≤ 1).

We study the direct relation between the degrees of approximation of Riemann integrable functions with respect to algebraic polynomials with average modulus of smoothness ${\tau }_{2}(f,{\rm{\Delta }}\frac{1}{\sqrt{j}})$ the locally global spaces (L_δ,P), (0 < P ≤ 1) wich is importance for the approximations theory.