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

doi:https://doi.org/10.1186/1687-1812-2013-324

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

Department of Telecommunications and Systems Engineering

Research output: Contribution to journal › Article › Research › peer-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 language	English
Article number	324
Journal	Fixed Point Theory and Applications
Volume	2013
DOIs	https://doi.org/10.1186/1687-1812-2013-324
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

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title = "Best proximity and fixed point results for cyclic multivalued mappings under a generalized contractive condition",

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. {\textcopyright}2013 De la Sen et al.; licensee Springer.",

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AU - Singh, Shyam Lal

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AU - Ibeas, Asier

AU - Agarwal, Ravi P.

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AB - 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.

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KW - Uniform convex Banach space

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