Some properties of distances and best proximity points of cyclic proximal contractions in metric spaces
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)

Date:	2014
Abstract:	This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping T: ∪ - A → ∪ - B (p ≥ 2), where A and B, i ∈ p - = { 1,2,⋯, p }, are nonempty subsets of X which satisfy T A ⊂ B, i ∈ p -, such that (X, d) is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed.
Grants:	Ministerio de Economía y Competitividad 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
Published in:	Abstract and applied analysis, Vol. 2014 (October 2014) , art. 914915, ISSN 1687-0409

DOI: 10.1155/2014/914915

12 p, 2.0 MB

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