Direct and Inverse Inequalities for Jackson Polynomials of 2-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 =) while in (1983) V.A.Popov and J.Szabados [3] (1 p  ) have proved a direct inequality for Jackson polynomials in L p-sp ace of 2-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 ,p) of 2-p eriodic 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 ,p ) in terms of the average modulus of continuity .