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

doi:https://doi.org/10.1186/1029-242X-2014-498

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

Department of Telecommunications and Systems Engineering

Research output: Contribution to journal › Article › Research › peer-review

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 language	English
Article number	498
Journal	Journal of Inequalities and Applications
Volume	2014
DOIs	https://doi.org/10.1186/1029-242X-2014-498
Publication status	Published - 26 Dec 2014

Keywords

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

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

abstract = "{\textcopyright} 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.",

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T1 - Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

AU - De la Sen, Manuel

AU - Ibeas, Asier

PY - 2014/12/26

Y1 - 2014/12/26

N2 - © 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.

AB - © 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.

KW - contractive and strictly contractive self-mappings

KW - convergence

KW - expansive

KW - fixed point

KW - non-expansive

KW - stability

KW - switched dynamic systems

U2 - https://doi.org/10.1186/1029-242X-2014-498

DO - https://doi.org/10.1186/1029-242X-2014-498

M3 - Article

VL - 2014

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

SN - 1025-5834

M1 - 498

ER -