Journal of the
Korean Mathematical Society
JKMS

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

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J. Korean Math. Soc. 2001; 38(3): 669-681

Printed May 1, 2001

Copyright © The Korean Mathematical Society.

A generalization of the Krasnoselskii-Petryshyn compression and expansion theorem: an essential map approach

Ravi P. Agarwal and Donal O'Regan

National University of Singapore and National University of Ireland

Abstract

This paper introduces the notions of essential and inessential maps for countably $\,k$--set contractive maps. These ideas enable us to establish a Krasnoselskii--Petryshyn compression and expansion theorem in a cone for countably $\,k$--set contractive maps.

Keywords: essential and inessential maps, countably $k$-set contractive maps, fixed point results

MSC numbers: 47H10

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