On some conditions connected with approximation in generalized Orlicz spaces (Q1824135)

Given a (b-a)-periodic function \(\phi\) (t,u) defined on \(R\times R^+\), consider the generalized Orlicz space \(L^{\phi}_{b-a}\) of (b-a)- periodic functions generated by \(\phi\). Many properties connected with problems of approximation for usual Orlicz spaces, i.e. spaces generated by functions \(\phi\) independent of t, may be transferred to generalized Orlicz spaces assuming \(\phi\) to satisfy some additional condition, which is indicated here. Some consequences of these facts are derived; among other things, some estimations for the averaged modulus of smoothness of functions such that \(f^{(k)}\in L^{\phi}_{b-a}\) are given. This paper is related to some other papers of the same author.