On a generalization of Horn's fixed point theorem
type: Item
instance of: scholarly article
title: On a generalization of Horn's fixed point theorem
zbMATH Open document ID: 0763.47027
DOI: 10.1016/0022-247X(92)90143-2
author: Falun Huang
author: Jin Liang
author: Tijun Xio
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The authors present the following theorem: Let \(X\) be a locally convex topological vector space, \(S_ 0\subset S_ 1\subset S_ 2\subset X\), with \(S_ 0\) and \(S_ 2\) compact convex, and \(S_ 1\) open relative to \(S_ 2\). Let \(f: S_ 2\to X\) be a continuous mapping such that for some positive integer \(m\), \(f^ j(S_ 1)\subset S_ 2\), \(1\leq j\leq m-1\); \(f^ j(S_ 1)\subset S_ 0\), \(m\leq j\leq 2m-1\). Then \(f\) has a fixed point in \(S_ 0\). This result is a generalization of \textit{W. A. Horn}'s fixed point theorem [Trans. Am. Math. Soc. 149, 391-404 (1970; Zbl 0201.462), Theorem 6].
reviewed by: R.Iino
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 60580
zbMATH Keywords: Horn's fixed point theorem
MaRDI profile type: Publication
cites work: Periodic solutions to functional differential equations
cites work: On a generalization of the Schauder fixed point theorem
cites work: Q3687202
cites work: An Asymptotic Fixed Point Theorem for a Locally Convex Space
cites work: Q3254057
cites work: Some Fixed Point Theorems for Compact Maps and Flows in Banach Spaces
cites work: Q5667036
full work available at URL: 0022-247x(92)90143-2
OpenAlex ID: W2093338364
description: scientific article; zbMATH DE number 60580