论文标题
在Orlicz空间中Durrmeyer-Smplampling类型运算符的收敛属性上
On the convergence properties of Durrmeyer-Sampling Type Operators in Orlicz spaces
论文作者
论文摘要
在这里，我们提供了由所谓的Durrmeyer采样类型系列给出的一般形式的采样类型运算符的融合处理。特别是我们在$ \ mathbb {r} $上提供了一个方向且均匀的收敛定理，在这种情况下，我们还使用要近似函数的连续性模量为近似值提供了定量估计值。然后，我们在Orlicz空间的一般设置$ l^φ（\ Mathbb {r}）$中获得模块化收敛定理。从后者的结果中，$ l^p（\ mathbb {r}）$ - 空间，$ l^α\ log^βl$中的收敛性，指数空间随之而来。最后，为具有特殊内核的几个采样序列提供了具有图形表示的应用和示例。
Here we provide a unifying treatment of the convergence of a general form of sampling type operators, given by the so-called Durrmeyer sampling type series. In particular we provide a pointwise and uniform convergence theorem on $\mathbb{R}$, and in this context we also furnish a quantitative estimate for the order of approximation, using the modulus of continuity of the function to be approximated. Then we obtain a modular convergence theorem in the general setting of Orlicz spaces $L^φ(\mathbb{R})$. From the latter result, the convergence in $L^p(\mathbb{R})$-space, $L^α\log^βL$, and the exponential spaces follow as particular cases. Finally, applications and examples with graphical representations are given for several sampling series with special kernels.
