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 further their study and present 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. Martín and P.L. Papini. We shall also use the modulus of convexity and the modulus of smoothness to give some estimates concerning our parameters. We also indicate some open problems
A study of perimeters for a class of triangles contained in the unit ball of normed spaces
Marco Baronti;Valentina Bertella;Pier Luigi Papini
2025-01-01
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 further their study and present 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. Martín and P.L. Papini. We shall also use the modulus of convexity and the modulus of smoothness to give some estimates concerning our parameters. We also indicate some open problems
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
