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Abstract and Applied Analysis
Volume 2014, Article ID 948749, 13 pages
Research Article

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

1Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644, Barrio Sarriena, 48940 Leioa, Spain
2Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona (UAB), 08193 Barcelona, Spain

Received 29 January 2014; Revised 27 May 2014; Accepted 28 May 2014; Published 22 June 2014

Academic Editor: Haydar Akca

Copyright © 2014 Manuel De la Sen and Asier Ibeas. 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 boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.