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Star-shaped Differentiable Functions and Star-shaped Differentials
  • ISSN号：1674-5647
  • 期刊名称：《数学研究通讯：英文版》
  • 时间：0
  • 分类：O13-19[理学—数学;理学—基础数学] U463.218.4[机械工程—车辆工程;交通运输工程—载运工具运用工程;交通运输工程—道路与铁道工程]
  • 作者机构：[1]School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, [2]School of Mathematical Sciences, Harbin Normal University, Harbin, 150080
  • 相关基金：Foundation item： The NSF （10771026） of China.
作者： PAN SHAO-RONG[1,2], ZHANG HONG-WEI[1], ZHANG LI-WEI[1]
关键词： 微函数, 差速器, 星型, 函数空间, 复合材料, 定理证明, 定向型, 导函数, The space of star-shaped sets, gauge function, isometrical isomorphism, directionally differentiable function, star-shaped differential, mean-value theorem
中文摘要：

基于在塑造星的集合的空间和连续确实同类的真实值的功能的空间之间的同晶型，塑造星方向性地可辨的功能微分被定义。公式为塑造星 pointwise 最大值和方向性地可辨的功能的一个有限数字的 pointwise 最小微分，并且一二方向性地可辨的功能合成被导出。而且，为方向性地可辨的功能的吝啬值的定理被表明。

英文摘要：

Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.

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期刊信息
  • 《数学研究通讯：英文版》
  • 中国科技核心期刊
  • 主管单位:教育部
  • 主办单位:吉林大学
  • 主编：尹景学
  • 地址：长春市前进大街2699号吉林大学数学研究所内
  • 邮编：130012
  • 邮箱：
  • 电话：0431-5166424
  • 国际标准刊号：ISSN：1674-5647
  • 国内统一刊号：ISSN：22-1369/O1
  • 邮发代号:12-134
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊
  • 被引量:5