Direct and inverse theorems are proved for approximation by bounded Vilenkin systems in weighted Orlicz spaces. The equivalence between the K-functional constructed with help of generalized derivative and three types of realizations functionals is established. We also obtain a simultaneous approximation result.

中文翻译：

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加权Orlicz空间中Vilenkin多项式的逼近。

通过加权的Orlicz空间中的有界Vilenkin系统证明了直接定理和逆定理是近似的。建立了借助广义导数构造的K函数与三种实现函数之间的等价关系。我们还获得了同时逼近的结果。