Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 648591, 13 pages
Research Article

Fixed Point Theorems for Middle Point Linear Operators in L1

Milena Chermisi1 and Anna Martellotti2

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.


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.