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

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

References

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