Behaviours. Convexity with respect to a behaviour

Abstract

The concept of behaviour of an object is largely used in order to make difference between things. As a mathematical concept, Elena Popoviciu used the term behaviour for the first time in 1965, on the occasion of a conference held at Cluj-Napoca “Babeş-Bolyai” University, without publishing it. The discussions on this theme have been reconsidered during the meetings of the Interdisciplinary Researches Laboratory of Cluj-Napoca “Babeş-Bolyai” University between 1980-1983. In this period, she wrote especially about the particular case of behaviours that are shapes of functions, in order to generalise the property of convexity of a function. The main results in this direction are written in the papers of E. Moldovan (1955, 1958,1959) and E. Popoviciu (1969, 1972, 1983). Her disciples, M. Ivan (1975, 1980, 1982) and R. Precup (1984, 1995) gave applications of this concept in interpolation and approximation.