Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 953091, 15 pages
Research Article

Stable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration

IIDP, Faculty of Science and Technology, University of the Basque Country, Campus of Leioa (Bizkaia), Aptdo. 644, Bilbao, Spain

Received 25 March 2010; Accepted 11 July 2010

Academic Editor: Dominguez Benavides

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.


This paper investigates the stability of iteration procedures defined by continuous functions acting on self-maps in continuous metric spaces. Some of the obtained results extend the contraction principle to the use of altering-distance functions and extended altering-distance functions, the last ones being piecewise continuous. The conditions for the maps to be contractive for the achievement of stability of the iteration process can be relaxed to the fulfilment of being large contractions or to be subject to altering-distance functions or extended altering functions.