Direct and Inverse Inequalities for Jackson Polynomials of 2ï°-Periodic Bounded Measurable Functions in Locally Clobal Norms

Abstract

Convergence prop erties of Jackson polynomials have been considered by Zugmund
[1,ch.X] in (1959) and J.Szbados [2], (p =ï‚¥) while in (1983) V.A.Popov and J.Szabados [3]
(1 ï‚£p ï‚£ ï‚¥) have proved a direct inequality for Jackson polynomials in L
p-sp ace of 2ï°-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
ï¤,p) of 2ï°-p eriodic bounded measurable functions (f Lï‚¥) 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
ï¤,p
) in terms of the average modulus of continuity .