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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:948749
    DOI: 10.1155/2014/948749
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    References listed on IDEAS

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    1. Juan R. Torregrosa & Ioannis K. Argyros & Changbum Chun & Alicia Cordero & Fazlollah Soleymani, 2013. "Iterative Methods for Nonlinear Equations or Systems and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-2, September.
    2. M. De la Sen & E. Karapinar, 2013. "Best Proximity Points of Generalized Semicyclic Impulsive Self‐Mappings: Applications to Impulsive Differential and Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Juan R. Torregrosa & Ioannis K. Argyros & Changbum Chun & Alicia Cordero & Fazlollah Soleymani, 2013. "Iterative Methods for Nonlinear Equations or Systems and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Debashis Dey & Amit Kumar Laha & Mantu Saha, 2013. "Approximate Coincidence Point of Two Nonlinear Mappings," Journal of Mathematics, Hindawi, vol. 2013, pages 1-4, March.
    5. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2013. "A Best Proximity Point Result in Modular Spaces with the Fatou Property," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Gani Stamov & Haydar Akca & Ivanka Stamova, 2013. "Uncertain Dynamical Systems: Analysis and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. M. De la Sen & E. Karapinar, 2013. "Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-16, October.
    8. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2013. "A Best Proximity Point Result in Modular Spaces with the Fatou Property," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-4, September.
    9. Gani Stamov & Haydar Akca & Ivanka Stamova, 2013. "Uncertain Dynamical Systems: Analysis and Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-2, June.
    10. M. De la Sen & A. Ibeas & S. Alonso-Quesada, 2013. "Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, October.
    11. Vadim Azhmyakov & Marco Angulo, 2011. "Applications of the strong approximability property to a class of affine switched systems and to relaxed differential equations with affine structure," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(11), pages 1899-1907.
    12. M. De la Sen & A. Ibeas & S. Alonso-Quesada, 2013. "Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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