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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2006; 43(1): 1-9

Printed January 1, 2006

Copyright © The Korean Mathematical Society.

Fixed points of countably condensing mappings and its application to nonlinear eigenvalue problems

In-Sook Kim

Sungkyunkwan University

Abstract

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Based on the Schauder fixed point theorem, we give a Leray-Schauder type fixed point theorem for countably condensing mappings in a more general setting and apply it to obtain eigenvalue results on condensing mappings in a simple proof. Moreover, we present a generalization of Sadovskii's fixed point theorem for countably condensing self-mappings due to S. J. Daher.

Keywords: fixed points, eigenvalues, countably condensing mappings, measures of noncompactness

MSC numbers: 47H10, 47J10, 47H09

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