Direct and inverse inequalities for Jackson polynomials of 2π- periodic bounded measurable functions in locally clobal norms

Abstract EN

Convergence properties of Jackson polynomials have been considered by Zugmund [1, ch.

X] in (1959) and J.

Szbados [2], (p = ∞) while in (1983) V.

A.

Popov and J.

Szabados [3] (1 ≤ p ≤ ∞) have proved a direct inequality for Jackson polynomials in Lp-space of 2 π-periodic bounded Riemann integrable functions (f ∈ R) in terms of some modulus of continuity. In 1991 S.

K.

Jassim proved direct and inverse inequality for Jackson polynomials in locally global norms (L δ, p) of 2 π -periodic bounded measurable functions (f ∈ L∞) in terms of suitable Peetre K-functional [4]. Now the aim of our paper is to proved direct and inverse inequalities for Jackson polynomials of (f ∈ L∞) in (L δ, p) in terms of the average modulus of continuity.