DOMÍNGUEZ BENAVIDES , Tomás

En la mayor parte de las aplicaciones de la Teoría de Sistemas Dinámicos (espacios de funciones, ecuaciones diferenciales, etc.) el espacio fase lleva aparejada, además de la estructura topológica, una estructura lineal compatible con esta topología. Esta no ha sido, sin embargo, utilizada nunca en la teoría clásica, que se limita a las...

The Fixed Point Theory for nonexpansive mappings is strongly based upon the geometry of the ambient Banach space. In section 1 we state the role which is played by the multidimensional convexity and smoothness in this theory. In section 2 we study the computation of the normal structure coefficient in finite dimensional lp-spaces and its...

No description

Se definen las matrices de Hadamard y se indican algunos problemas referentes a su existencia, construcción y unicidad. Se mostrarán algunos ejemplos de aplicaciones de las matrices de Hadamard para resolver problemas de muy diferentes áreas de las matemáticas, concretamente: obtención de determinantes maximales, diseño de pesadas, detección...

In this paper we define a new geometric constant M(X) in Banach spaces such that X has the fixed point property for nonexpansive mappings if M(X) > 1. We prove that M(X) •_ WCS(X), the inequality being strict in many important classes of Banach spaces and we obtain lower bounds for M(X) based upon either the modulus of near uniform smoothness...

Assume that X is a Banach space such that its Szlenk index Sz X is less than or equal to the first infinite ordinal ω. We prove that X can be renormed in such a way that X with the resultant norm satisfies R X < 2, where R · is the García-Falset coefficient. This leads us to prove that if X is a Banach space which can be continuously embedded...

No description

In this survey, we comment on the current status of several questions in Metric Fixed Point Theory which were raised by W. A. Kirk in 1995.

In this paper we derive an existence theorem for the implicit defferential equation F(t, x,x') = 0 ; x(to) = are where F is a β-Lipschitz or α-Lipschitz operator in the second variable. The existence of maximal and unlimited solution is studied and a continuous dependence theorem is proved.

In this paper, we prove that for any number λ < (√33−3)/2, any separable space X can be renormed in such a way that X satisfies the weak fixed point property for non-expansive mappings and this property is inherited for any other isomorphic space Y such that the Banach-Mazur distance between X and Y is less than λ. We also prove that any, in...

No description

Fixed Point Theory for multivalued mappings has many useful applications in Applied Sciences, in particular, in Game Theory and Mathematical Economics. Thus, it is natural to try of extending the known fixed point results for single-valued mappings to the setting of multivalued mappings. Some theorems of existence of fixed points of...

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...