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Direct and Inverse Inequalities for Jackson Polynomials of 2-Periodic Bounded Measurable Functions in Locally Clobal Norms | ||
| Ibn Al-Haitham Journal For Pure And Applied Science | ||
| Article 1, Volume 23, Issue 2, 2010, Pages 141-151 | ||
| Authors | ||
| ; | ||
| Abstract | ||
| 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-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-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,p) in terms of the average modulus of continuity. | ||
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