Volume 2,
Issue 1, 2001
Article
10
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COMPLETE
SYSTEMS OF INEQUALITIES
1M.A.
HERNANDEZ CIFRE, 1G.
SALINAS AND 2S.S.
GOMIS
1DEPARTAMENTO
DE MATEMÁTICAS
UNIVERSIDAD DE MURCIA
CAMPUS DE ESPINARDO
30100 MURCIA, SPAIN
E-Mail: mhcifre@um.es
E-Mail: guisamar@navegalia.com
2DEPARTAMENTO DE ANÁLISIS
MATEMÁTICO
Y MATEMÁTICA APLICADA
UNIVERSIDAD DE ALICANTE
CAMPUS DE SAN VINCENTE DEL RASPEIG
APDO. DE CORREOS 99
E-03080 ALICANTE, SPAIN
E-mail: Salvador.Segura@ua.es
Received 12 September, 2000; accepted 29 November 2000.
Communicated by: S.S. Dragomir
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ABSTRACT.
In this paper we summarize the known results and the main tools concerning complete systems of inequalities for families of convex sets. We discuss also the possibility to use these systems to determine particular subfamilies of planar convex sets with specific geometric significance. We also analyze complete systems of inequalities for 3-rotationally symmetric planar convex sets concerning the area, the perimeter, the circumradius, the inradius, the diameter and the minimal width; we give a list of new inequalities concerning these parameters and we point out which are the cases that are still open.
Key words:
Inequality, complete
system,
planar convex
set, area, perimeter,
diameter, width,
inradius, circumradius.
2000 Mathematics Subject
Classification:
62G30,
62H10.
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