Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

Manuel De la Sen, Asier Ibeas

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6 Citations (Scopus)

Abstract

© 2014, Sen and Ibeas; licensee Springer. This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.
Original languageEnglish
Article number498
JournalJournal of Inequalities and Applications
Volume2014
DOIs
Publication statusPublished - 26 Dec 2014

Keywords

  • contractive and strictly contractive self-mappings
  • convergence
  • expansive
  • fixed point
  • non-expansive
  • stability
  • switched dynamic systems

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