LORENZO RAMÍREZ , Josefa

"En el Capítulo 1 de la Memoria se recoge la información que consideramos necearia para la valoración y compresión de los distintos aspectos de la Teoría Métrica del Punto Fijo que en ella se discuten. En algunas secciones, paralelamente a la introducción

In this survey we present an exposition of the development during the last decade of metric fixed point theory on hyperconvex metric spaces. Therefore we mainly cover results where the conditions on the mappings are metric. We will recall results about proximinal nonexpansive retractions and their impact into the theory of best approximation...

Let X be a Banach space, C a weakly compact convex subset of X and T : C → C an asymptotically nonexpansive mapping. Under the usual assumptions on X which assure the existence of fixed point for T, we prove that the set of fixed points is a nonexpansive retract of C. We use this result to prove that all known theorems about existence of fixed...

Let X be a nearly uniformly convex Banach space, C a convex closed bounded subset of X and T : C → 2 C a multivalued nonexpansive mapping with convex compact values. We prove that T has a fixed point. This result improves former results in Domínguez Benavides, T., P. Lorenzo, Fixed point theorems for multivalued nonexpansive mappings without...

This paper is devoted to state some fixed point results for multivalued mappings in modular vector spaces. For this purpose, we study the uniform noncompact convexity, a geometric property for modular spaces which is similar to nearly uniform convexity in the Banach spaces setting. Using this property, we state several new fixed point theorems...

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Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the non-strict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The non-strict...

In this work we prove a new strong convergence result of the regularized successive approximation method given by yn+1 = qnz0 + (1 − qn)T n yn, n = 1, 2, ..., where limn→∞ qn = 0 and X∞ n=1 qn = ∞, for T a total asymptotically nonexpansive mapping, i.e., T is such that kT nx − T n yk ≤ kx − yk + k (1) n φ(kx − yk) + k (2) n , where k 1 n and...

We study the existence of fixed points in the context of uniformly convex geodesic metric spaces, hyperconvex spaces and Banach spaces for single and multivalued mappings satisfying conditions that generalize the concept of nonexpansivity. Besides, we use the fixed point theorems proved here to give common fixed point results for commuting mappings.

We extend some known fixed point results for mappings satisfying Kannan type conditions to the context of K-metric spaces. Firstly, we prove a common fixed point result for noncommuting maps. A generalization of Kannan's fixed point theorem is given in some class of spaces including K-metric spaces.