On asymptotic centres and fixed point theorems for set-valued nonexpansive mappings
type: Item
instance of: scholarly article
title: On asymptotic centres and fixed point theorems for set-valued nonexpansive mappings
zbMATH Open document ID: 0576.47032
author: D. Sahani
author: R. K. Bose
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: First a fixed point theorem concerning set-valued nonexpansive and weakly inward mappings on unbounded domain is proved by imposing a mild boundedness condition on the mappings. This theorem extends a result of \textit{W. A. Kirk} and \textit{W. O. Ray} [Stud. Math. 64, 125-127 (1979; Zbl 0412.47033)] for single valued mapping. Next a fixed point theorem of a set-valued mapping on nonconvex domain is proved. \textit{K. Yanagi} [Pac. J. Math. 87, 233-240 (1980; Zbl 0408.47042)] has proved a fixed point theorem in this direction where the domain of the mapping is weakly compact starshaped subset of a uniformly convex Banach space. With Lami Dozo's (1983) new concepts of asymptotic centre and radius, the authors have proved a similar theorem replacing the uniform convexity assumption on the space with some geometric assumption on the domain.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 3921328
zbMATH Keywords: fixed point theorem concerning set-valued nonexpansive and weakly
zbMATH Keywords: inward mappings on unbounded domain
zbMATH Keywords: set-valued mapping on nonconvex domain
zbMATH Keywords: asymptotic centre and radius
zbMATH Keywords: fixed point theorem concerning set-valued nonexpansive and weakly inward mappings on unbounded domain
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3921328