Best proximity and fixed point results for cyclic multivalued mappings under a generalized contractive condition

Manuel De La Sen, Shyam Lal Singh, Madjid Eshaghi Gordji, Asier Ibeas, Ravi P. Agarwal

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)

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. ©2013 De la Sen et al.; licensee Springer.
Original languageEnglish
Article number324
JournalFixed Point Theory and Applications
Volume2013
DOIs
Publication statusPublished - 1 Jan 2013

Keywords

  • Best proximity points
  • Cyclic self-mappings
  • Fixed points
  • Metric space
  • Multi-control
  • Multivalued self-mappings
  • Uniform convex Banach space

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