Averaged modulus of smoothness and two-sided monotone approximation in Orlicz spaces

Abstract

The paper deals with basic properties of averaged modulus of smoothness in Orlicz spaces $L^*_\varphi$. Some direct and inverse two-sided approximation problems in $L^*_\varphi$ are proved. In the last section, some inequalities concerning monotone two sided approximation by trigonometric polynomials in $L^*_\varphi$ are considered.