Modules of convexity, characteristic of convexity and fixed point theorems
type: Item
instance of: scholarly article
title: Modules of convexity, characteristic of convexity and fixed point theorems
zbMATH Open document ID: 0654.47041
author: Hajime Ishihara
author: Wataru Takahashi
published in: Kodai Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Various numerical parameters have been introduced to describe the geometric structure of a Banach space E; classical examples are the modulus of convexity \(\delta\) (E;\(\epsilon)\), the characteristic of convexity \(\epsilon_ 0(E)\), and the normal structure coefficient N(E). For instance, if \(\epsilon_ 0(E)=0\) \([\epsilon_ 0(E)<1,\epsilon_ 0(E)<2,N(E)>1\), resp.], then E is uniformly convex [has normal structure, is reflexive, has normal structure and is reflexive, resp.]. In the present paper, the authors define corresponding characteristic \(\delta\) (C;\(\epsilon)\), \(\epsilon_ 0(C)\), and N(C) for arbitrary convex subsets C of E, and prove some fixed point theorems. This extends previous work of W. L. Bynum, K. Goebel, V. I. Gurarij, E. Moluta, E. Casini, and others.
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 46A55
zbMATH DE Number: 4067690
zbMATH Keywords: modulus of convexity
zbMATH Keywords: characteristic of convexity
zbMATH Keywords: normal structure coefficient
zbMATH Keywords: uniformly convex
zbMATH Keywords: fixed point theorems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037414
OpenAlex ID: W1973093604
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DOI: 10.2996/KMJ/1138037414
description: scientific article; zbMATH DE number 4067690