The Direct and Converse Theorems for Best Approximation of Algebraic Polynomial in 𝑳𝒑,𝜶(𝑿)

Abstract

The direct and inverse algebraic polynomials approximation theorems in weighted spaces of unbounded functions are proved by using modulus of smoothness. Also, we obtain sharp Jackson ( direct ) inequality of algebraic approximation of unbounded functions in terms modulus of smoothness . In addition, constructive characterization of modulus of smoothness are considered.