An index theory for countably \(P\)-concentrative \(J\) maps
type: Item
instance of: scholarly article
title: An index theory for countably \(P\)-concentrative \(J\) maps
zbMATH Open document ID: 1063.47057
DOI: 10.1016/S0893-9659(03)90127-3
author: Ravi P. Agarwal
author: Donal O'Regan
published in: Applied Mathematics Letters
publication date: 2004-06-15T00:00:00Z
review text: This article deals with a modification of Andres-Gabor-Gorniewicz' index theory of compact maps \(T\) in Fréchet space, \(T \in J(\overline{U},C)\) or, in other words, \(T\) is semicontinuous with nonempty, compact, \(\infty\)-proximally connected values; here \(C\) is a closed convex subset of \(E\), \(U\) an open bounded subset of \(C\). The authors consider the case when \(T\) is an only countably \(P\)-concentrative map. For such maps \(T\) with \(x \neq Tx\) for \(x \in \partial U\), the index \(I(T,C,R,U)\) is defined in two standard ways; then the existence property, the homotopy property, and the additivity property are proved.
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 2075538
zbMATH Keywords: fixed point index
zbMATH Keywords: multimaps
zbMATH Keywords: retraction
zbMATH Keywords: countably \(P\)-concentrative map
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2075538