Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2005; 42(6): 1205-1213

Printed November 1, 2005

Copyright © The Korean Mathematical Society.

Eigenvalues of countably condensing admissible maps

In-Sook Kim

Sungkyunkwan University

Abstract

Applying a fixed point theorem for compact admissible maps due to G\'orniewicz, we prove that under certain conditions each countably condensing admissible maps in Fr\'echet spaces has a positive eigenvalue. This result has many consequences, including the well-known theorem of Krasnoselskii.

Keywords: eigenvalues, countably condensing maps, admissible maps, measures of noncompactness

MSC numbers: 47J10, 47H09, 54C60