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Coincidence Points of Function Pairs Based on Compactness Properties

Published online by Cambridge University Press:  25 July 2002

M. Väth
M. Väth
Affiliation:
University of Würzburg, Department of Mathematics, Am Hubland, D-97074 Würzburg, Germany e-mail: vaeth@mathematik.uni-wuerzburg.de
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Abstract

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Existence theorems for the equation F(x)=\varphi (x) are proved when F is a function with “good” surjective properties and \varphi satisfies certain compactness conditions on countable subsets of the space. Also results for certain homotopic perturbations of the equation are obtained. The results lead to various fixed point theorems of Darbo type for F=id, but they are also applicable if F acts between different spaces. Also the inclusions F(x)\in \varphi (x) (resp. F(x)\subseteq \varphi (x)) for multivalued functions \varphi (resp. F and \varphi) are studied. There are some connections with the theory of 0-epi maps.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 2 , May 2002 , pp. 209 - 230
Copyright
2002 Glasgow Mathematical Journal Trust