Generalized convexity and invexity without vector space structure
type: Item
instance of: scholarly article
zbMATH Open document ID: 0972.52001
author: Giuseppe Caristi
author: Massimiliano Ferrara
publication date: 2001-11-22T00:00:00Z
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 52A41
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 1583840
zbMATH Keywords: convexlike function
zbMATH Keywords: mean convex function
zbMATH Keywords: invexity
MaRDI profile type: Publication
title: Generalized convexity and invexity without vector space structure
review text: \textbf{E.Heil (Darmstadt)}: The concept of a convex function may be generalized to functions defined on nonlinear spaces by demanding that for any \(x_1\), \(x_2\) there is an \(x_0\) such that \(f(x_0)\leq tf(x_1)+(1+ t)f(x_2)\) for some or all \(t\in (0,1)\). This and similar concepts and the relations between them are considered in this paper.NEWLINENEWLINENEWLINE\textbf{Rita Pini (Milano)}: The authors present a review and state the relationship among the concepts of \(t\)--convexlikeness, weak convexity, \(t\)--convexity, that are widely used in proving minimax results. These concepts apply to families of functions defined on an arbitrary nonempty set, and are essentially based on uniform convexlike properties of the functions of the family. In the end, the concepts of convexity, weak convexity and weak convexlikeness are generalized via a mean function.NEWLINENEWLINEFor the entire collection see [Zbl 0948.00038].
reviewed by: Erhard Heil
description: scientific article