Linearly and directionally bounded weak-star closed sets and the AFPP

  • Tomás Domínguez BenavidesEmail author
  • Maria A. Japón
  • Jeimer Villada Bedoya


Linearly bounded and directionally bounded closed convex sets play a very relevant role in metric fixed point theory [12, 14, 16]. In reflexive spaces both collections of sets are identical and this fact characterizes the reflexivity of the space [14, 16]. Since closed convex sets are weakstar closed in reflexive spaces, it is natural to ask about the relationship between linearly bounded and directionally bounded sets in the case of a non-reflexive dual space if we assume, in addition, that the set is weak-star closed. We will show two divergent answers to this question depending on certain topological and isometric properties of the underlying dual Banach space.


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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • Tomás Domínguez Benavides
    • 1
    Email author
  • Maria A. Japón
    • 1
  • Jeimer Villada Bedoya
    • 2
  1. 1.Departamento de Análisis MatemáticoUniversidad de SevillaSevillaSpain
  2. 2.Centro de Investigación en MatemáticasJalisco s/n, ValencianaGuanajuato, Gto.Mexico

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