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 language | English |
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Article number | 324 |
Journal | Fixed Point Theory and Applications |
Volume | 2013 |
DOIs | |
Publication status | Published - 1 Jan 2013 |
Keywords
- Best proximity points
- Cyclic self-mappings
- Fixed points
- Metric space
- Multi-control
- Multivalued self-mappings
- Uniform convex Banach space