Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 568072, 19 pages
http://dx.doi.org/10.1155/2011/568072
Research Article

On the Extensions of Krasnoselskii-Type Theorems to 𝑝 -Cyclic Self-Mappings in Banach Spaces

M. De la Sen

Instituto de Investigacion y Desarrollo de Procesos, Universidad del Pais Vasco, Campus de Bizkaia, P.O. Box 644, 48080 Bilbao, Spain

Received 4 March 2011; Revised 22 June 2011; Accepted 26 June 2011

Academic Editor: Zhen Jin

Copyright © 2011 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

A set of 𝑛 𝑝 (≥2)-cyclic and either continuous or contractive self-mappings, with at least one of them being contractive, which are defined on a set of subsets of a Banach space, are considered to build a composed self-mapping of interest. The existence and uniqueness of fixed points and the existence of best proximity points, in the case that the subsets do not intersect, of such composed mappings are investigated by stating and proving ad hoc extensions of several Krasnoselskii-type theorems.