中文摘要：

算子逼近论是函数逼近理论的重要分支之一,具有较深的理论意义和广泛的应用前景。相比较于连续函数空间和L^p空间,Orlicz空间比它们都＂大＂,尤其是由不满足Δ2条件的N函数生成的Orlicz空间是L^p空间的实质性的扩充,其拓扑结构比L^p空间复杂的多,因此在Orlicz空间内研究算子逼近问题具有一定的拓展意义。本文研究了一种Szasz-MirakjanBaskakov算子在Orlicz空间内的逼近问题,利用连续模、Holder不等式N函数的凸性及Jensen不等式等工具,得到了该算子在Orlicz空间内逼近的正逆定理.

英文摘要：

operator approximation theory is one of the most important branches of function approximation theory. It has deep theoret- ical significance and wide application prospect. Compared with the continuous function of space and space, Orlicz space is big than them, especially by generation do not satisfy the conditions of the function of the Orlicz space is a space of substantial expansion, the topological structure is more complicated than space, so in the Orlicz space of operator approximation problem has a certain meaning. This paper studies the approximation problem of a Szasz - Mirakjan - Baskakov operator in Orlicz spaces, by using the continuous mode, Holder inequality and Jensen inequality of convex function etc, are obtained. The inverse theorem of approximation operator in Orlicz spaces.