• 대한수학회지
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• 제46권2호
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• pp.271-279
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• 2009

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.

• 대한수학회보
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• 제47권1호
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• pp.121-129
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• 2010

Using a degree theory for countably condensing multivalued maps, we show that under certain conditions an invariance of domain theorem holds for countably condensing or countably k-contractive multivalued vector fields.

• 대한수학회지
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• 제42권6호
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• pp.1205-1213
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• 2005

Applying a fixed point theorem for compact admissible maps due to Gorniewicz, we prove that under certain conditions each count ably condensing admissible maps in Frechet spaces has a positive eigenvalue. This result has many consequences, including the well-known theorem of Krasnoselskii.

• 대한수학회지
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• 제45권1호
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• pp.151-161
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• 2008

We prove that a countably condensing operator defined on a closed wedge in a Banach space has a fixed point if it is strictly quasibounded, by using an index theory for such operators. From this, the existence of eigenvalues and surjectivity are deduced.