Electron. J. Differential Equations, Vol. 2016 (2016), No. 253, pp. 1-9.

An extension of the compression-expansion fixed point theorem of functional type

Richard I. Avery, Douglas R. Anderson, Johnny Henderson

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