Richard I. Avery, Douglas R. Anderson, Johnny Henderson
Abstract:
In this article we use an interval of functional type as the underlying
set in our compression-expansion fixed point theorem argument which can
be used to exploit properties of the operator to improve conditions that
will guarantee the existence of a fixed point in applications.
An example is provided to demonstrate how intervals of functional type
can improve conditions in applications to boundary value problems.
We also show how one can use suitable k-contractive conditions to prove
that a fixed point in a functional-type interval is unique.
Submitted July 11, 2016. Published September 21, 2016.
Math Subject Classifications: 47H10.
Key Words: Fixed-point theorem; k-contractive; expansion; compression.
An addendum was posted on October 6, 2016. It modifies Theorem 3.1. See the last three pages of this article.
Show me the PDF file (199 KB), TEX file for this article.
 |
Richard I. Avery College of Arts and Sciences Dakota State University Madison, South Dakota 57042, USA email: rich.avery@dsu.edu |
|---|---|
 |
Douglas R. Anderson Department of Mathematics Concordia College Moorhead, MN 56562, USA email: andersod@cord.edu |
 |
Johnny Henderson Department of Mathematics Baylor University Waco, TX 76798, USA email: Johnny_Henderson@baylor.edu |
Return to the EJDE web page