Best proximity and fixed point results for cyclic multivalued mappings under a generalized contractive condition
De la Sen, Manuel (Universidad del País Vasco. Departamento de Electricidad y Electrónica)
Singh, Shyam Lal (Pt. Lalit Mohan Sharma Government Post-Graduate College (Rishikesh, Índia))
Gordji, Madjid Eshaghi (Semnan University. Department of Mathematics)
Ibeas, Asier (Universitat Autònoma de Barcelona. Departament de Telecomunicació i Enginyeria de Sistemes)
Agarwal, Ravi P. (King Abdulaziz University. Department of Mathematics)

Date:	2013
Abstract:	This paper is devoted to investigating the existence of fixed points and best proximity points of multivalued cyclic self-mappings in metric spaces under a generalized contractive condition involving Hausdorff distances. Some background results for cyclic self-mappings or for multivalued self-mappings in metric fixed point theory are extended to cyclic multivalued self-mappings. An example concerned with the global stability of a time-varying discrete-time system is also discussed by applying some of the results obtained in this paper. Such an example includes the analysis with numerical simulations of two particular cases which are focused on switched discrete-time control and integrate the associate theory in the context of multivalued mappings.
Grants:	Ministerio de Educación y Ciencia DPI2012-30651
Rights:	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.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Best proximity points ; Cyclic self-mappings ; Fixed points ; Metric space ; Multi-control ; Multivalued self-mappings ; Uniform convex Banach space
Published in:	Fixed Point Theory and Applications, Vol. 2013 (November 2013) , art. 324, ISSN 1687-1812

DOI: 10.1186/1687-1812-2013-324

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