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<p>The <i>p</i>-uniform degree parameters including James, Schäffer and Gao–Lau constants for the unit spheres in <i>p</i>-normed spaces (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_416_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\(0&lt;p\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>p</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>) are introduced and investigated. Concisely, their general properties are presented; the exact values of them in several special spaces are estimated; and detailed relations among these constants and the modulus of <i>p</i>-rotundity are revealed. Additionally, some inequalities between isomorphic spaces are established.</p>

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On the geometry of balls in p-normed spaces: James, Schäffer and Gao–Lau constants

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Jian-Zhong Xiao,
  • Xing-Hua Zhu

摘要

The p-uniform degree parameters including James, Schäffer and Gao–Lau constants for the unit spheres in p-normed spaces ( \(0<p\le 1\) 0 < p ≤ 1 ) are introduced and investigated. Concisely, their general properties are presented; the exact values of them in several special spaces are estimated; and detailed relations among these constants and the modulus of p-rotundity are revealed. Additionally, some inequalities between isomorphic spaces are established.