dc.creator | Domínguez Benavides, Tomás | es |
dc.creator | Japón Pineda, María de los Ángeles | es |
dc.date.accessioned | 2018-12-19T07:53:14Z | |
dc.date.available | 2018-12-19T07:53:14Z | |
dc.date.issued | 2018-12 | |
dc.identifier.citation | Domínguez Benavides, T. y Japón Pineda, M.d.l.Á. (2018). Komlós' Theorem and the Fixed Point Property for affine mappings. Proceedings of the American Mathematical Society, 146 (12), 5311-5322. | |
dc.identifier.issn | 0002-9939 | es |
dc.identifier.issn | 1088-6826 | es |
dc.identifier.uri | https://hdl.handle.net/11441/81111 | |
dc.description.abstract | Assume that X is a Banach space of measurable functions for which Koml´os’ Theorem holds. We associate to any closed convex bounded subset C of X a coefficient t(C) which attains its minimum value when C is closed for the topology of convergence in measure and we prove some fixed point results for affine Lipschitzian mappings, depending on the value of t(C) ∈ [1, 2] and the value of the Lipschitz constants of the iterates. As a first consequence, for every L < 2, we deduce the existence of fixed points for affine uniformly L-Lipschitzian mappings defined on the closed unit ball of L1[0, 1]. Our main theorem also provides a wide collection of convex closed bounded sets in L
1([0, 1]) and in some other spaces of functions, which satisfy the fixed point property for affine nonexpansive mappings. Furthermore, this property is still
preserved by equivalent renormings when the Banach-Mazur distance is
small enough. In particular, we prove that the failure of the fixed point
property for affine nonexpansive mappings in L1(µ) can only occur in
the extremal case t(C) = 2. Examples are displayed proving that our
fixed point theorem is optimal in terms of the Lipschitz constants and
the coefficient t(C). | es |
dc.description.sponsorship | Ministerio de Economía y Competitividad | es |
dc.description.sponsorship | Junta de Andalucía | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | American Mathematical Society | es |
dc.relation.ispartof | Proceedings of the American Mathematical Society, 146 (12), 5311-5322. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Measurable function spaces | es |
dc.subject | Fixed point | es |
dc.subject | Affine Lipschitzian mappings | es |
dc.subject | Equivalent norms | es |
dc.subject | µ-a.e. convergence | es |
dc.subject | Convergence in measure | es |
dc.title | Komlós' Theorem and the Fixed Point Property for affine mappings | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | MTM2015-65242-C2-1-P | es |
dc.relation.projectID | FQM-127 | es |
dc.relation.publisherversion | https://www.ams.org/journals/proc/2018-146-12/S0002-9939-2018-14201-X/S0002-9939-2018-14201-X.pdf | es |
dc.identifier.doi | 10.1090/proc/14201 | es |
dc.contributor.group | Universidad de Sevilla. FQM127: Análisis Funcional no Lineal | es |
idus.format.extent | 12 p. | es |
dc.journaltitle | Proceedings of the American Mathematical Society | es |
dc.publication.volumen | 146 | es |
dc.publication.issue | 12 | es |
dc.publication.initialPage | 5311 | es |
dc.publication.endPage | 5322 | es |
dc.contributor.funder | Ministerio de Economía y Competitividad (MINECO). España | |
dc.contributor.funder | Junta de Andalucía | |