Cai Qing-Bo, Xu Xiao-Wei
1School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, China.
2School of Computer and Data Engineering, Ningbo Institute of Technology, Zhejiang University, Ningbo, China.
J Inequal Appl. 2018;2018(1):241. doi: 10.1186/s13660-018-1821-9. Epub 2018 Sep 14.
In this paper, we introduce a new family of generalized Bernstein operators based on integers, called -Bernstein operators, denoted by . We investigate a Kovovkin-type approximation theorem, and obtain the rate of convergence of to any continuous functions . The main results are the identification of several shape-preserving properties of these operators, including their monotonicity- and convexity-preserving properties with respect to . We also obtain the monotonicity with and of .
在本文中，我们引入了一族基于整数的新的广义伯恩斯坦算子，称为 - 伯恩斯坦算子，记为 。我们研究了一个科罗夫金型逼近定理，并得到了 对任意连续函数的收敛速度。主要结果是确定了这些算子的几个保形性质，包括它们关于 的保单调性和保凸性性质。我们还得到了 关于 和 的单调性。
