Generalized Cyclic p-Contractions and p-Contraction Pairs Some Properties of Asymptotic Regularity Best Proximity Points, Fixed Points
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)

Data:	2022
Resum:	This paper studies a general (Formula presented. ) -contractive condition of a self-mapping (Formula presented. ) on (Formula presented. ), where (Formula presented. ) is either a metric space or a dislocated metric space, which combines the contribution to the upper-bound of (Formula presented. ), where (Formula presented. ) and (Formula presented. ) are arbitrary elements in (Formula presented. ) of a weighted combination of the distances (Formula presented. ) (Formula presented. ) and (Formula presented. ). The asymptotic regularity of the self-mapping (Formula presented. ) on (Formula presented. ) and the convergence of Cauchy sequences to a unique fixed point are also discussed if (Formula presented. ) is complete. Subsequently, (Formula presented. ) generalized cyclic (Formula presented. ) -contraction pairs are discussed on a pair of non-empty, in general, disjoint subsets of (Formula presented. ). The proposed contraction involves a combination of several distances associated with the (Formula presented. ) -pair. Some properties demonstrated are: (a) the asymptotic convergence of the relevant sequences to best proximity points of both sets is proved; (b) the best proximity points are unique if the involved subsets are closed and convex, the metric is norm induced, or the metric space is a uniformly convex Banach space. It can be pointed out that both metric and a metric-like (or dislocated metric) possess the symmetry property since their respective distance values for any given pair of elements of the corresponding space are identical after exchanging the roles of both elements.
Drets:	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.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Publicat a:	Symmetry, Vol. 14, Issue 11 (November 2022) , art. 2247, ISSN 2073-8994

DOI: 10.3390/sym14112247

28 p, 6.2 MB

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