LÓPEZ ACEDO , Genaro

El primero de los capítulos recoge únicamente los resultados que hemos tenido que utilizar para el desarrollo del trabajo que se presentas, estos resultados han sido extraídos fundamentalmente del libro de K. Deimling (6).

A useful property of the Brouwer degree relates the degree of a composition of maps to the degree of each map. This property, which can be generalized for the Leray Schauder degree and in some cases for the A-proper maps is called the Product Formula. In G. Lopez, On the topological degree for A-compact mappings, J. Math. Anal. Appl. 159(2),...

Ministerio de Ciencia e Innovación

In this paper we develop an axiomatic theory for the multivalued degree that preserves the basic properties of the classical degree. We apply it to obtain fixed point theroems and existence of solution fix) = p. We give a method to extend this degree.

We give a sufficient and necessary condition concerning a Browder's convergence type theorem for uniformly asymptotically regular one-parameter nonexpansive semigroups in Hilbert spaces.

Convergence of fixed point sets of multivalued nonexpansive mappings is studied under both the Mosco and Hausdorff senses. A characterization for *- nonexpansive multivalued mappings is given. Also a counterexample is constructed to show a negative answer to a question raised by A. Canbtti, G. Marino and P. Pibtramala.

W. A. Kirk has recently proved a constructive fixed point theorem for continuous mappings in compact hyperconvex metric spaces [6]. In the present work we use the concept of hyperconvex hull of a metric space to obtain a noncompact counterpart of Kirk's result.

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...

In this paper, we use techniques which originate from proof mining to give rates of asymptotic regularity and metastability for a sequence associated to the composition of two firmly nonexpansive mappings.

Two iterative algorithms for nonexpansive mappings on Hadamard manifolds, which are extensions of the well-known Halpern's and Mann's algorithms in Euclidean spaces, are proposed and proved to be convergent to a fixed point of the mapping. Some numerical examples are provided.

This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.

We analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform betweenness property and use it in the study of a discrete lion and man game with an ε -capture criterion. In particular, we prove that in uniformly convex bounded domains the lion...

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...

We consider the optimization problem (PA) infx∈X{f(x) + g(Ax)} where f and g are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y, respectively, and A is a linear operator from X to Y . By using the properties of the epigraph of the conjugated functions, some sufficient and necessary conditions for...

The space lp,q is simply the space lp but renormed by 1 Ixlp,q =(11x+llg + IIx-IIg);, ß E where II'[Ip is the usual lp norm and x + and x- are the positive and negative. parts of x, respectively. Bynum used lp,1 and Smith and Turett used 12,1 to show that neither normal structure nor uniform normal structure is a self dual property for Banach...

In [13] T. Zamfirescu, Fixed point theorems in metric spaces, Arch. Math. 23 (1972), 292–298. Zamfirescu gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan and Chatterjea. In this paper, we follow the ideas of Dugundji and Granas to extend Zamfirescu's fixed point theorem to the class of weakly...

Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard manifolds. In this paper we prove that these conditions are mutually equivalent and they hold if and only if the Hadamard manifold is isometric to the Euclidean space....

In the present paper, we consider inexact proximal point algorithms for finding singular points of multivalued vector fields on Hadamard manifolds. The rate of convergence is shown to be linear under the mild assumption of metric subregularity. Furthermore, if the sequence of parameters associated with the iterative scheme converges to 0, then...

We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and is completely different from previous ones on...

The relationship between monotonicity and accretivity on Riemannian manifolds is studied in this paper and both concepts are proved to be equivalent in Hadamard manifolds. As a consequence an iterative method is obtained for approximating singularities of Lipschitz continuous, strongly monotone mappings. We also establish the equivalence...

Some relationships between the Kuratowski's measure of noncompactness, the ball measure of noncompactness and the d-separation of the points of a set are studied in special classes of Banach spaces. These relations are applied to compare operators which are contractive for these measures.

No description