Approximating Polynomials for Functions of Weighted Smirnov-Orlicz Spaces
Open Access
- 8 February 2012
- journal article
- research article
- Published by Hindawi Limited in Journal of Function Spaces and Applications
- Vol. 2012, 1-41
- https://doi.org/10.1155/2012/982360
Abstract
Let and be, respectively, bounded and unbounded components of a plane curve satisfying Dini's smoothness condition. In addition to partial sum of Faber series of belonging to weighted Smirnov-Orlicz space (), we prove that interpolating polynomials and Poisson polynomials are near best approximant for . Also considering a weighted fractional moduli of smoothness, we obtain direct and converse theorems of trigonometric polynomial approximation in Orlicz spaces with Muckenhoupt weights. On the bases of these approximation theorems, we prove direct and converse theorems of approximation, respectively, by algebraic polynomials and rational functions in weighted Smirnov-Orlicz spaces and .Keywords
This publication has 19 references indexed in Scilit:
- Approximation by polynomials and rational functions in weighted rearrangement invariant spacesJournal of Mathematical Analysis and Applications, 2008
- Improved Inverse Theorems in Weighted Lebesgue and Smirnov SpacesBulletin of the Belgian Mathematical Society - Simon Stevin, 2007
- APPROXIMATION BY INTERPOLATING POLYNOMIALS IN SMIRNOV-ORLICZ CLASSJournal of the Korean Mathematical Society, 2006
- Approximation in weighted Smirnov-Orlicz classesKyoto Journal of Mathematics, 2006
- Approximation in Smirnov-Orlicz classesGlasnik Matematicki, 2005
- Approximation by p-Faber-Laurent Rational Functions in the Weighted Lebesgue SpacesCzechoslovak Mathematical Journal, 2004
- Approximation by p -Faber polynomials in the weighted Smirnov class Ep( G,ω ) and the Bieberbach polynomialsConstructive Approximation, 2001
- On the degree of polynomial approximation in Ep(D)Journal of Approximation Theory, 1977
- On analytic functions of Smirnov-Orlicz classesStudia Mathematica, 1968
- Integrated continuity conditions and degree of approximation by polynomials or by bounded analytic functionsTransactions of the American Mathematical Society, 1959