TY  - JOUR
T1  - A study of perimeters for a class of triangles contained in the unit ball of normed spaces
AU  - Baronti, Marco
AU  - Bertella, Valentina
AU  - Papini, Pier Luigi
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.33205/cma.1663969
JF  - Constructive Mathematical Analysis
JO  - CMA
PB  - Tuncer ACAR
WT  - DergiPark
SN  - 2651-2939
SP  - 135
EP  - 145
VL  - 8
IS  - 3
LA  - en
AB  - 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.
KW  - Triangles
KW  - equilateral
KW  - parameters
KW  - Minkowski planes
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UR  - https://doi.org/10.33205/cma.1663969
L1  - https://dergipark.org.tr/en/download/article-file/4717990
ER  -