Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 648591, 13 pages
doi:10.1155/2008/648591
Research Article
Fixed Point Theorems for Middle Point Linear Operators in L1
1Fachbereich Mathematik, Universität Duisburg-Essen, Lotharstraße 65, 47057 Duisburg, Germany
2Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Perugia, Italy
Received 3 February 2008; Revised 11 August 2008; Accepted 8 September 2008
Academic Editor: Klaus Schmitt
Copyright © 2008 Milena Chermisi and Anna Martellotti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We introduce the notion of middle point linear operators. We prove a fixed point result for
middle point linear operators in L1. We then present some examples and, as an application,
we derive a Markov-Kakutani type fixed point result for commuting family of
α-nonexpansive
and middle point linear operators in L1.