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http://dx.doi.org/10.4134/JKMS.2009.46.2.271

EIGENVALUES OF COUNTABLY CONDENSING MAPS  

Kim, In-Sook (DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY)
Kim, Yun-Ho (DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY)
Kwon, Sung-Hui (DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.2, 2009 , pp. 271-279 More about this Journal
Abstract
Using an index theory for countably condensing maps, we show the existence of eigenvalues for countably k-set contractive maps and countably condensing maps in an infinite dimensional Banach space X, under certain condition that depends on the quantitative haracteristic, that is, the infimum of all $k\;{\geq}\;1$ for which there is a countably k-set-contractive retraction of the closed unit ball of X onto its boundary.
Keywords
eigenvalues; countably condensing maps; fixed point index;
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