超二次函数的碎形视角与概率估计的概括概率估计
Saad Ihsan Butt1, Dawood Khan1, Youngsoo Seol2
1Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan.
PloS one
|February 11, 2025
概括
这项研究介绍了关于分数集的概括超二次函数,开发了新的不等式. 这些新发现提供了比凸函数更高的精细化,并且在碎形空间中有应用.
科学领域:
- 数学分析的数学分析
- 碎形几何学 碎形几何学
背景情况:
- 一般化的超二次函数在数学分析中至关重要.
- 分数集对函数分析和不平等发展提出了独特的挑战.
研究的目的:
- 介绍和分析一个新的类型的概括的超二次函数在分数集.
- 在这些函数的基础上开发新的普遍不平等.
- 探索这些不平等在碎形空间的实际含义.
主要方法:
- 关于分数集合上概括的超二次函数的定义和表征.
- 推导一般化的詹森的,转换詹森的,默瑟詹森的,和赫米特-哈达马德的不等式.
- 通过数值计算,图形表示和用通用凸函数进行比较分析进行验证.
主要成果:
- 介绍关于分数集的概括超二次函数.
- 建立新的泛式不等式,与泛式凸函数的不等式相比,具有更高的精细化.
- 在概率预期和分数空间内的特殊方法中的适用性证明.
结论:
- 新开发的不平等在现有文献中提供了显著的改进和扩展.
- 一般化的超二次函数为分数集上的不等式提供了一个更精细的框架.
- 这项研究为碎形分析及其应用领域的进一步探索开辟了道路.
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