Electron. J. Diff. Eqns., Vol. 2008(2008), No. 22, pp. 1-12.

Functional compression-expansion fixed point theorem

Richard Avery, Johnny Henderson, Donal O'regan

This paper presents a generalization of the fixed point theorems of compression and expansion of functional type. As an application, the existence of a positive solution to a second order conjugate boundary value problem is considered. We conclude with an extension to multivalued maps.

Submitted January 31, 2008. Published February 22, 2008.
Math Subject Classifications: 47H10.
Key Words: Fixed-point theorems; cone; positive solutions; multivalued maps.

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Richard Avery
College of Arts and Sciences, Dakota State University
Madison, South Dakota 57042, USA
email: rich.avery@dsu.edu
Johnny Henderson
Department of Mathematics, Baylor University
Waco, Texas 76798, USA
email: Johnny_Henderson@baylor.edu
Donal O'regan
Department of Mathematics
National University of Ireland
Galway, Ireland
email: donal.oregan@nuigalway.ie

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