Convergence properties and fixed points of two general iterative schemes with composed maps in banach spaces with applications to guaranteed global stability

Manuel De La Sen, Asier Ibeas

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Abstract

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. © 2014 Manuel De la Sen and Asier Ibeas.
Original languageEnglish
Article number948749
JournalAbstract and Applied Analysis
Volume2014
DOIs
Publication statusPublished - 1 Jan 2014

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