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Second and third order forward difference operator: what is in between?
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 2.9 ) Pub Date : 2021-03-22 , DOI: 10.1007/s13398-021-01015-5
Jennifer Bravo , Carlos Lizama , Silvia Rueda

In this article, we present a new geometrical notion for a real-valued function defined in a discrete domain that depends on a parameter \(\alpha \ge 2.\) We give examples to illustrate connections between convexity and this new concept. We then prove two criteria based on the sign of the discrete fractional operator of a function u, \(\Delta ^{\alpha }u\) with \(2 \le \alpha < 4.\) Two examples show that the given criteria are optimal with respect to the established geometrical notion.



中文翻译:

二阶和三阶前向差分算子:两者之间是什么?

在本文中,我们为离散域中定义的依赖于参数\(\ alpha \ ge 2. \)的实值函数提供了一种新的几何概念。我们提供一些示例来说明凸度和这个新概念之间的联系。然后,我们基于函数u的离散分数运算符\\(\ Delta ^ {\ alpha} u \)\(2 \ le \ alpha <4. \)证明两个准则。两个示例表明,给定关于已建立的几何概念,最佳标准是最佳的。

更新日期:2021-03-22
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