Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 438614, 25 pages
doi:10.1155/2010/438614
Research Article

Some Fixed Point Properties of Self-Maps Constructed by Switched Sets of Primary Self-Maps on Normed Linear Spaces

M. De la Sen

Instituto de Investigacion y Desarrollo de Procesos, Universidad del Pais Vasco, Campus of Leioa (Bizkaia), Aptdo. 644 Bilbao, 48080 Bilbao, Spain

Received 15 September 2009; Revised 3 March 2010; Accepted 25 March 2010

Academic Editor: L. Górniewicz

Copyright © 2010 M. De la Sen. 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

This paper is devoted to the investigation of the existence of fixed points in a normed linear space X endowed with a norm ‖⋅‖ for self-maps f from T×X to X which are constructed from a given class of so-called primary self- maps being also from T×X to X. The construction of the self-maps of interest is performed via a so-called switching rule which is a piecewise-constant map from a set T to some finite subset of the positive integers or a sequence map which domain in some discrete subset of T.