Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 42, pp. 1-11.

Title: Operator type expansion-compression fixed point theorem

Authors: Douglas R. Anderson (Concordia College, Moorhead, MN, USA)
         Richard I. Avery (Dakota State Univ., Madison, SD, USA)
	 Johnny Henderson (Baylor Univ., Waco, TX, USA)
	 Xueyan Liu (Baylor Univ., Waco, TX, USA)
	 
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.