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

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  • Manuel De la Sen
  • Asier Ibeas

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.

Suggested Citation

  • Manuel De la Sen & Asier Ibeas, 2014. "Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, June.
    • Handle: RePEc:hin:jnlaaa:948749
    DOI: 10.1155/2014/948749
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