A study of perimeters for a class of triangles contained in the unit ball of normed spaces

Year 2025, Volume: 8 Issue: 3, 135 - 145

Marco Baronti , Valentina Bertella , Pier Luigi Papini

https://doi.org/10.33205/cma.1663969

Abstract

Recently, A. Ahmad, Y. Fu and Y. Li considered a class of triangles inscribed in the unit ball of a Banach space; they introduced two parameters, based on the perimeter of these triangles, and indicated a few results. Here we deepen their study, we give several new results and we compare these parameters with other ones. We consider triangles $T(x,y,z)$ with $x,y,z$ in the unit sphere and such that $x+y+z=0$. We compare this class with the one of equilateral triangles, studied in a recent paper by J. Alonso, P. Mart{\'i}n and P.L. Papini. We shall use also the modulus of convexity and the modulus of smoothness to give some estimates concerning our parmeters. We also indicate some open problems.

Keywords

Triangles, equilateral, parameters, Minkowski planes

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