对k-harmonically凸函数的新增扩展及其在信息科学中的应用
Asfand Fahad1,2,3, Shigeru Furuichi4,5, Zammad Ali3
1School of Software, Pingdingshan University, Pingdingshan, China.
PloS one
|July 1, 2025
概括
本研究介绍了k-harmonically convex函数 (k-HCFs) 和它们的扩展,用于信息科学中的实际应用. 对于信息理论测量来说,我们得出了新的不平等,从而增强了k-HCF的实用性.
科学领域:
- 凸的分析 凸的分析
- 信息科学 信息科学 信息科学
- 优化理论 优化理论
背景情况:
- 凸起式分析具有广泛的应用,但很少有一般化的凸起式函数具有实际影响.
- 现有的凸函数概括的有限适用性阻碍了应用领域的进步.
研究的目的:
- 介绍和探索一个新的凸度概念:k-harmonically convex functions (k-HCFs). 介绍和探索一个新的凸度概念:k-harmonically convex functions (k-HCFs). 介绍和探索一个新的凸度概念:k-harmonically convex functions (k-HCFs). 介绍和探索一个新的凸度概念:k-harmonically convex functions (k-HCFs).
- 使用参数化和区间值函数 (IVFs) 扩展k-HCFs.
- 将这些扩展应用于信息理论措施,并建立新的不平等.
主要方法:
- 开发了一个k-harmonically凸函数的r-parameterized扩展.
- 将k-HCF扩展到使用完整顺序关系的区间值函数.
- 对衍生扩展的研究性质和不等式.
- 导出了 Tsallis ,Shannon 和 Tsallis 相对的下界.
主要成果:
- 引入并分析了r参数化和间隔值的k-HCFs.
- 建立了基于Cr顺序的k-HCF的Jensen,Mercer和Hermite-Hadamard类型不等式.
- 使用扩展函数对关键信息理论指标推导下限.
结论:
- 对k-harmonically凸函数的新型扩展在信息科学中提供了更广泛的应用.
- 由此产生的不平等提供了重要的新见解,并重现已知的结果.
- k-HCF在推进信息科学应用方面具有相当大的潜力.
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