Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

Relaciones amorosas de pareja en las trayectorias vitales de las mujeres encarceladas

[ES]La tesis doctoral analiza las experiencias amorosas de pareja de mujeres encarceladas, con el doble objetivo de visibilizar a las mujeres presas en el ámbito de las ciencias sociales y de introducir las especificidades de las mujeres encarceladas en los debates sociológicos y feministas acerca del amor. Las escasas aproximaciones al amor entre las mujeres presas han tendido a explicar sus relaciones de pareja desde el concepto de “dependencia emocional”, que, como se muestra en la tesis, presenta dos debilidades básicas, de un lado la tendencia a la psicologización y patologización de cuestiones de claro sustrato social; de otro la homogeneización de experiencias que presentan gran diversidad. Otra debilidad de ciertos análisis sobre las mujeres presas y aquellas excluidas socialmente, es que se han basado en concepciones sexistas acerca de las mujeres transgresoras como “malas mujeres”, por considerar que no cumplen con las expectativas culturales y sociales asociadas a los supuestos atributos de género. Esta tesis doctoral adopta una epistemología basada en la crítica feminista que busca modelos analíticos alejados de los estereotipos y la estigmatización de las mujeres transgresoras. Desde una perspectiva metodológica cualitativa, el trabajo de campo fue desarrollado en la cárcel de Nanclares de Oca (País Vasco) durante el 2008. Desarrollé un trabajo etnográfico de observación participante y entrevistas en profundidad semiestructuradas que elaboraban información sobre aspectos relativos a sus trayectorias de vida (familia de origen, vivienda, empleo, nivel educativo, situación penal y penitenciaria, estado de salud, etc.) y sus experiencias amorosas de pareja. En mi análisis, he rastreado la diversidad y variabilidad de las experiencias amorosas de las mujeres presas, el impacto del encarcelamiento en sus trayectorias amorosas y en la configuración de su intimidad, los elementos que hacen para estas mujeres del amor un “cautiverio”, y al mismo tiempo, las estrategias “liberadoras” que despliegan en sus desarrollos afectivos. El amor puede constituir un cautiverio para las mujeres ya que favorece la acomodación a unos roles de género que definen a las mujeres como dependientes y carentes de libertad. Al mismo tiempo, el amor se puede entender como una “estrategia emocional”, una forma de superar las consecuencias del encierro y de lograr ciertos estándares de “normalización” social, en un contexto en que se encuentran excluidas socialmente y fuertemente estigmatizadas.

Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces

In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.