一类广义的Bezier算子的保形性质
Shape Preserving Properties of Generalized Bezier Type Operators
DOI: 10.12677/PM.2023.139264, PDF,    国家自然科学基金支持
作者: 董 惠：河北师范大学数学科学学院，河北 石家庄 ；齐秋兰*：河北师范大学数学科学学院，河北 石家庄 ；河北省计算数学与应用重点实验室，河北 石家庄
关键词: Bezier型算子；单调性；凸性；星形性；Bezier Type Operator； Monotonicity； Convexity； Starlikeness
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。
Abstract: 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.
文章引用：董惠, 齐秋兰. 一类广义的Bezier算子的保形性质[J]. 理论数学, 2023, 13(9): 2587-2595. https://doi.org/10.12677/PM.2023.139264

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