一类广义的Bezier算子的保形性质  

Shape Preserving Properties of Generalized Bezier Type Operators

作　　者：董惠 齐秋兰[2,3] 

机构地区：[1]河北师范大学数学科学学院,河北 石家庄 [2]河北师范大学数学科学学院,河北 石家庄 [3]河北省计算数学与应用重点实验室,河北 石家庄

出　　处：《理论数学》2023年第9期2587-2595,共9页Pure Mathematics

摘　　要：本文对一种以广义二项分布的概率密度函数作为基函数构造的广义Bezier型算子性质进行研究,得到了这类算子在单调性、凸性、星形性、半可加性和光滑性等方面的保形性质。最后,通过具体数值实例验证新方法的有效性及灵活性。In this paper, we study the properties of a kind of Bezier type operators constructed with the probability density function of a generalized binomial distribution as the basis functions, and obtain the shape preserving properties of this kind of operator concerning monotonicity, convexity, starlikeness, semi-additivity, and smoothness. Finally, through specific numerical examples, we verify the effectiveness and flexibility of the new method.

关 键 词：Bezier型算子 单调性 凸性 星形性 

分 类 号：O17[理学—数学]