Douglas R. Anderson, Richard I. Avery, Johnny Henderson, Xueyan Liu
Abstract:
This article presents an alternative to the compression
and expansion fixed point theorems of functional type by
using operators and functions to replace the functionals
and constants that are used in functional compression
and expansion fixed point theorems. Only portions of
the boundaries are required to be mapped outward or
inward in the spirit of the original work of Leggett-Williams.
We conclude with an application verifying the existence of
a positive solution to a second-order boundary-value problem.
Submitted October 27, 2010. Published March 25, 2011.
Math Subject Classifications: 47H10.
Key Words: Fixed-point theorems; Leggett-Williams;
expansion; compression; positive solutions.
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Douglas R. Anderson Department of Mathematics and Computer Science Concordia College, Moorhead, MN 56562, USA email: andersod@cord.edu |
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Richard I. Avery College of Arts and Sciences, Dakota State University Madison, South Dakota 57042, USA email: rich.avery@dsu.edu |
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Johnny Henderson Department of Mathematics, Baylor University Waco, TX 76798, USA email: Johnny_Henderson@baylor.edu |
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Xueyan (Sherry) Liu Department of Mathematics, Baylor University Waco, TX 76798-7328, USA email: Xueyan_Liu@baylor.edu |
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