Now showing items 1-9 of 9

    • Icon

      A continuation method for weakly contractive mappings under the interior condition  [Article]

      Ariza Ruiz, David; Jiménez Melado, Antonio (Hindawi, 2009)
      Recently, Frigon proved that, for weakly contractive maps, the property of having a fixed point is invariant by a certain class of homotopies, obtaining as a consequence a Leray-Schauder alternative for this class of maps ...
    • Icon

      A continuation method for weakly Kannan maps  [Article]

      Ariza Ruiz, David; Jiménez Melado, Antonio (SpringerOpen, 2010)
      The first continuation method for contractive maps in the setting of a metric space was given by Granas. Later, Frigon extended Granas theorem to the class of weakly contractive maps, and recently Agarwal and O’Regan have ...
    • Icon

      A fixed point theorem for weakly Zamfirescu mappings  [Article]

      Ariza Ruiz, David; Jiménez Melado, Antonio; López Acedo, Genaro (Elsevier, 2011-03-01)
      In [13] T. Zamfirescu, Fixed point theorems in metric spaces, Arch. Math. 23 (1972), 292–298. Zamfirescu gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan and Chatterjea. In ...
    • Icon

      Existence and uniqueness of solution to several kinds of differential equations using the coincidence theory  [Article]

      Ariza Ruiz, David; García Falset, Jesús (Mathematical Society of the Republic of China, 2015)
      The purpose of this article is to study the existence of a coincidence point for two mappings defined on a nonempty set and taking values on a Banach space using the fixed point theory for nonexpansive mappings. Moreover, ...
    • Icon

      Firmly nonexpansive mappings in classes of geodesic spaces  [Article]

      Ariza Ruiz, David; Leustean, Laurentiu; López Acedo, Genaro (American Mathematical Society, 2014)
      Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and ...
    • Icon

      Métodos de continuacíón: de licenciado a doctor  [Presentation]

      Ariza Ruiz, David (2013)
    • Icon

      Rate of convergence under weak contractiveness conditions  [Article]

      Ariza Ruiz, David; Briseid, Eyvind Martol; Jiménez Melado, Antonio; López Acedo, Genaro (Casa Cartii de Stiinta, 2013)
      We introduce a new class of selfmaps T of metric spaces, which generalizes the weakly Zamfirescu maps (and therefore weakly contraction maps, weakly Kannan maps, weakly Chatterjea maps and quasi-contraction maps with ...
    • Icon

      The asymptotic behavior of the composition of firmly nonexpansive mappings  [Article]

      Ariza Ruiz, David; López Acedo, Genaro; Nicolae, Adriana (Springer, 2015-11)
      In this paper we provide a unified treatment of some convex minimization problems, which allows for a better understanding and, in some cases, improvement of results in this direction proved recently in spaces of curvature ...
    • Icon

      Wardowski conditions to the coincidence problem  [Article]

      Ariza Ruiz, David; García Falset, Jesús; Sadarangan, Kishin (Frontiers Media, 2015-08-31)
      In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ X such that Tp = Sp, where X is a nonempty set, Y is a complete metric space, and T, S:X → Y are two mappings ...