Kyungpook Mathematical Journal

  • 제63권1호
  • /
  • Pages.61-78
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  • 2023
  • /
  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some Geometric Constants Related to the Heights and Midlines of Triangles in Banach Spaces

  • Dandan Du (Department of Mathematics, Sun Yat-sen University) ;
  • Yuankang Fu (Department of Mathematics, Sun Yat-sen University) ;
  • Zhijian Yang (Department of Mathematics, Sun Yat-sen University) ;
  • Yongjin Li (Department of Mathematics, Sun Yat-sen University)
  • 투고 : 2022.04.19
  • 심사 : 2022.10.07
  • 발행 : 2023.03.31
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초록

In this paper, we introduce two new geometric constants related to the heights of triangles: ∆H(X) and ∆h(X, I). We also propose two new geometric constants, ∆m(X) and ∆M(X), related to the midlines of equilateral triangles, and discuss the relation between the heights and midlines in equilateral triangles. We give estimates for these geometric constants in terms of other geometric parameters, and the geometric constants are used to discuss geometric properties such as uniform non-squareness, uniform normal structure, and the fixed point property.

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과제정보

This work was supported by the National Natural Science Foundation of P. R. China (Nos.11971493 and 12071491).

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