On Monch type multi-valued maps and fixed points
type: Item
instance of: scholarly article
title: On Monch type multi-valued maps and fixed points
zbMATH Open document ID: 1124.47033
author: Bapurao C. Dhage
published in: Applied Mathematics Letters
publication date: 2007-05-04T00:00:00Z
review text: The author presents some fixed point theorems for a (compact convex)-valued multimap \(T\) in a Banach space \(X\) satisfying the following condition: if \(A\) is a countable subset of \(X\), then \(A \subseteq \overline {\text{conv}} (C\cup T(A))\) for a given relatively compact set \(C \subset X\) implies that \(A\) is relatively compact. Reviewer's remark: In the reviewer's opinion, the correctness of the main results of the paper is not quite clear, since the compactness of the set \(C^*\) is not well justified in the proof of Theorem 2.1.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5149464
zbMATH Keywords: fixed point
zbMATH Keywords: multivalued map
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: condensing map
zbMATH Keywords: Mönch-type maps
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
full work available at URL: j.aml.2006.06.013
OpenAlex ID: W2066556499
cites work: Q3883053
cites work: Q5708812
cites work: Q5697726
cites work: Multi-valued operators and fixed point theorems in Banach algebras. I
cites work: Fixed points of compact multifunctions
cites work: Q4367585
cites work: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces
cites work: Q3706043
DOI: 10.1016/J.AML.2006.06.013
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description: scientific article; zbMATH DE number 5149464