On approximation in weighted Smirnov-Orlicz classes

Abstract

In this work, we investigate the approximation problems in weighted Smirnov-Orlicz classes. We prove a direct theorem for polynomial approximation of functions in certain subclasses of weighted Smirnov-Orlicz classes. The direct theorem is proved in terms of the modulus of smoothness. Also, from the main theorem some results are obtained. In the proof of the main theorem, a Jackson-Dzjadyk polynomial is used. © 2012 Taylor and Francis Group, LLC.