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Last name: FERNÁNDEZ LEÓN
First name: Aurora
In this paper we improve and extend some best proximity point results concerning the so- called proximal contractions. Specifically, compactness assumptions under the sets A and B are removed to consider completeness conditions instead.
El primer capítulo de este trabajo es de carácter preliminar y en él se reúnen fundamentalmente los conceptos más elementales y, en su mayoría, no originales que hemos estimado necesarios para una adecuada lectura y comprensión de toda la Memoria. También
Given A and B two nonempty subsets in a metric space, a mapping T : A ∪ B → A ∪ B is relatively nonexpansive if d(T x, T y) ≤ d(x, y) for every x ∈ A, y ∈ B. A best proximity point for such a mapping is a point x ∈ A ∪ B such that d(x, T x) = dist(A,B). In this work, we extend the results given in [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal...
We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibility problem for two sets in a nonlinear context. We show that weak convergence results from Hilbert spaces find natural counterparts in spaces of constant curvature....
Let A and B be two nonempty subsets of a metric space X. A mapping T : A[B ! A[B is said to be noncyclic if T(A) A and T(B) B. For such a mapping, a pair (x; y) 2 A B such that Tx = x, Ty = y and d(x; y) = dist(A;B) is called a best proximity pair. In this paper we give some best proximity pair results for noncyclic mappings under certain...
In this paper we show that some of the recent results on ¯xed point for CAT(0) spaces still hold true for CAT(1) spaces, and so for any CAT(k) space, under natural boundedness conditions. We also introduce a new notion of convergence in geodesic spaces which is related to the ¢-convergence and applied to study some aspects on the geometry of...
In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We do it from two different approaches, leading each one of them to different results which complete, if not improve, other similar results in the theory. Results in this paper...
Este trabajo forma parte de una investigación más amplia que tiene por objeto caracterizar cómo construyen conjeturas y demostraciones matemáticas los investigadores en matemáticas cuando investigan. Desde la filosofía de las matemáticas y la propia educación matemática, son cada vez más numerosas las recomendaciones que sugieren estudiar a...
We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for setvalued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the...
This paper studies how four primary-school in-service teachers develop the mathematical practices of conjecturing and proving. From the consideration of professional development as the legitimate peripheral participation in communities of practice, these teachers' mathematical practices have been characterised by using a theoretical framework...
En este capítulo se presenta un estudio sobre el conocimiento matemático de los estu diantes para maestro de Educación Primaria. Esta investigación parte de la consideración de que los futuros maestros no solo deben aprender conceptos matemáticos, definiciones, teoremas, etc., sino también las prácticas matemáticas a través de las cuales se...
In this paper, we study how undergraduate students define 3D geometrical solids. With this aim, we have identified the routines that are present in the discourse of the students when describing and defining these solids. These routines are one of the properties that characterise the mathematical discourse in the theory of commognition (Sfard...
En este trabajo estudiamos el proceso de definir de estudiantes universitarios para profesor a través del análisis del discurso matemático. Concretamente, nos centraremos en los resultados que hemos obtenido al analizar dicho discurso cuando los estudiantes definen cuerpos geométricos tridimensionales. Nuestra investigación adopta una...