对于区间值函数和应用的Ostrowski和Čebyšev类型不等式
Jing Guo1,2, Xianjun Zhu1,3,4, Wenfeng Li1
1School of Software Engineering, Jinling Institute of Technology, Nanjing, P. R. China.
PloS one
|September 25, 2023
概括
这项研究为区间值函数引入了新的Ostrowski和Čebyšev类型不等式,扩展了经典分析. 这些发现为方程规则的误差估计提供了实际应用,增强了数学方法.
科学领域:
- 数学分析的数学分析
- 设定值分析 设定值分析
背景情况:
- 奥斯特罗夫斯基和切比舍夫的不等式在古典分析中是基本的.
- 非加法积分不等式,包括Sugeno和Choquet积分,是广泛适用的.
- 设定值分析将经典分析与经济学和控制理论中的应用概括起来.
研究的目的:
- 为区间值函数建立特定的奥斯特罗夫斯基和Cebyšev类型不等式.
- 将不等式理论扩展到间隔分析领域.
- 通过应用来证明这些不平等的实用性.
主要方法:
- 基于现有的经典形式,开发新的区间值不等式.
- 设定价值分析技术的应用.
- 使用衍生不等式,对二次法则的误差估计.
主要成果:
- 成功确定了区间值函数的新型Ostrowski和Čebyšev类型不等式.
- 衍生不等式为分析区间值函数提供了一个框架.
- 有效估计了正方形规则的误差极限.
结论:
- 这篇论文成功地将Ostrowski和Čebyšev不等式扩展到区间值函数.
- 结果对数值集成和错误分析具有实际意义.
- 提出的数学方法是适用的,并通过示例来证明.
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