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

Journal of inequalities and applications

Manuel De la Sen¹ 

关键词: expansive;    non-expansive;    contractive and strictly contractive self-mappings;    switched dynamic systems;    convergence;    fixed point;    stability;   

DOI  :  10.1186/1029-242X-2014-498

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY