On Some Boundedness and Convergence Properties of a Class of Switching Maps in Probabilistic Metric Spaces with Applications to Switched Dynamic Systems
De la Sen, Manuel (Universidad del País Vasco. Departamento de Electricidad y Electrónica)
Ibeas, Asier (Universitat Autònoma de Barcelona. Departament de Telecomunicació i Enginyeria de Sistemes)

Data:	2015
Resum:	This paper investigates some boundedness and convergence properties of sequences which are generated iteratively through switched mappings defined on probabilistic metric spaces as well as conditions of existence and uniqueness of fixed points. Such switching mappings are built from a set of primary self-mappings selected through switching laws. The switching laws govern the switching process in between primary self-mappings when constructing the switching map. The primary self-mappings are not necessarily contractive but if at least one of them is contractive then there always exist switching maps which exhibit convergence properties and have a unique fixed point. If at least one of the self-mappings is nonexpansive or an appropriate combination given by the switching law is nonexpansive, then sequences are bounded although not convergent, in general. Some illustrative examples are also given.
Ajuts:	Ministerio de Economía y Competitividad DPI2012-30651 Ministerio de Economía y Competitividad DPI2013-47825-C3-1-R
Nota:	Altres ajuts: Gobierno Vasco (IT378-10) i Universidad del País Vasco (UFI 2011/07)
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Boundedness ; Convergence properties ; Existence and uniqueness ; Fixed points ; Nonexpansive ; Probabilistic metric spaces ; Switching law ; Switching process
Publicat a:	Mathematical Problems in Engineering, Vol. 2015 (2015) , art. 836283, ISSN 1563-5147

DOI: 10.1155/2015/836283

15 p, 2.2 MB

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