The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings

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 bounded above. For this purpose, we analyze the asymptotic behavior of compositions of finitely many firmly nonexpansive mappings in the setting of $p$-uniformly convex geodesic spaces focusing on asymptotic regularity and convergence results

A Continuation Method for Weakly Kannan Maps

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 given the corresponding result for a certain type of quasicontractions which includes maps of Kannan type. In this note we introduce the concept of weakly Kannan maps and give a fixed point theorem, and then a continuation method, for this class of maps

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

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, this type of results will be applied to obtain the existence of solutions for some classes of ordinary differential equations.Ministerio de Economía y CompetitividadJunta de Andalucí

Constructivismo en ciencias: pensamiento del alumnado versus pensamiento del profesorado

Se plantea en este trabajo la necesidad de concebir el constructivismo como una teoría epistemológica y didáctica válida para describir y orientar los procesos de desarrollo tanto del profesorado como del alumnado. Para ello, se describen brevemente algunas características básicas de las concepciones de los alumnos en los procesos de aprendizaje científico, de la evolución y cambio de las mismas, así como de las concepciones de los profesores en aras de una construcción significativa del conocimiento profesional. Desde esta perspectiva, se pone el énfasis en aquellos estudios que se han preocupado por analizar las concepciones de los profesores acerca de los procesos de pensamiento de los alumnos en ciencias, para finalizar con una serie de posibles implicaciones.This paper aims the peed to conceive constructivism view as an epistemological theory and suitable didactic to describe and line up the development processes for teachers and students. Some basic characteristics from the students' conceptions in the scientific learning processes are briefiy described, also the developmentand changing of these features. Similarly, the teachers' conceptions are analyzed to get a meaningful making of the professional knowledge. From this perspective, those studies that were concerned to analyze teachers' conceptions on students processes in science are emphasized. Finally, some potential implications are discussed

Wardowski conditions to the coincidence problem

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 satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration process to the above coincidence problem as well as a rate of convergence for this iteration scheme. Finally, we shall apply our results to study the existence and uniqueness of a solution as well as the convergence of the Picard-Juncgk iteration process toward the solution of a second order differential equation.Ministerio de Economía y CompetitividadJunta de Andalucí

Firmly nonexpansive mappings in classes of geodesic spaces

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 the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations.Junta de AndalucíaRomanian National Authority for Scientific ResearchDirección General de Enseñanza Superio

Actividad física como estrategia educativa para mejorar el rendimiento escolar

Currently, there is a great social concern for the low levels of school performance among the Spanish young people compared to other European countries. The practice of physical activity (PA) has recently been used as a stimulant to improve the cognitive performance in young people and to have positive repercussions on the academic performance (Ruiz-Ariza et al., 2017). The present research aims to conceptualize the relationship between PA and cognition, as well as to associate different physical qualities with better or worse school performance, and thus to be able to make decisions about the kind of PA more adequate to foment from the educative and familiar areas. We used multiple linear regressions adjusting for age, sex, body mass index, and educational level of mothers, to observe the relationship between each fitness component, and school performance. Our findings are in line with previous literature, and show that a higher physical fitness is associated with better school performance (Santana et al., 2016). The PA practice increases the production of irisine in muscle, a protein that is key to the brain and learning. In addition, improvements in fitness improves brain-derived neurotrophic factor, cerebral blood flow, neuron production and the connection between them (Adkins et al., 2006), improving executive functions and stimulating learning. In conclusion, our study suggests that it is necessary to strengthen the daily PA practice from educational centers, as well as to raise awareness among families and society about its promotion. Besides, novel active teaching methodologies are presented as an opportunity to include the movement in any subject and increase class motivation, emotions, and release stress or anxiety, making a greater performance to each subject, and obtaining a higer overall cognitive performance.Actualmente existe una gran preocupación social por los bajos niveles de rendimiento escolar entre los jóvenes españoles en comparación con otros países europeos. La práctica de actividad física (AF) ha sido utilizada recientemente como estimulante para mejorar el rendimiento cognitivo de los jóvenes y repercutir positivamente sobre el académico (Ruiz-Ariza et al., 2017). El presente trabajo pretende conceptualizar dicha relación entre AF y cognición, así como asociar diferentes cualidades físicas con un mejor o peor rendimiento escolar, y poder así tomar decisiones sobre el tipo de AF más adecuado a fomentar desde el ámbito educativo y también familiar. Usamos regresiones lineales múltiples ajustando por edad, sexo, índice de masa corporal y nivel de estudios de las madres, para observar la relación entre cada componente de condición física, y el rendimiento escolar. Nuestros hallazgos van en la línea de la literatura previa, y muestran que una mayor condición física se asocia con mejor rendimiento escolar (Santana et al., 2016). La práctica de AF aumenta la producción de irisina en el músculo, una proteína que es clave para el cerebro y el aprendizaje. Además, un mayor fitness mejora el factor neurotrófico derivado del cerebro, el riego sanguíneo cerebral, la producción de neuronas y la conexión entre ellas (Adkins et al. 2006), mejorando las funciones ejecutivas y estimulando el aprendizaje. Como conclusión, nuestro trabajo sugiere que es necesario potenciar la práctica diaria de AF desde los Centros educativos, así como concienciar a las familias y a la sociedad en general de su promoción. Además, nuevas metodologías activas de enseñanza se presentan como una oportunidad para incluir el movimiento en cualquier asignatura y aumentar la motivación por la clase, conectar emociones, y liberar el estrés o la ansiedad, sacándole un mayor rendimiento a cada materia, y obteniendo un mayor rendimiento total