Volume 2,  Issue 1, 2001

Article 10

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


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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