Axiomática para el grado muitivaluado

First published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales in volume 82, number 2, published by the Real Academia de Ciencias Exactas, Físicas y Naturales.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

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

Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces

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.Dirección General de Enseñanza SuperiorJunta de AndalucíaGrants-in-Aid for Scientific Research (Japanese Ministry of Education, Culture, Sports, Science and Technology

On a result of W. A. Kirk

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

Equilibrium problems on Riemannian manifolds with applications

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 this topic in the literature. As applications, the corresponding results for the mixed variational inequality and the Nash equilibrium are obtained. Moreover, we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem. In particular, correct proofs are provided for the results claimed in J. Math. Anal. Appl. 388, 61-77, 2012 (i.e., Theorems 3.5 and 4.9 there) regarding the existence of the mixed variational inequality and the domain of the resolvent for the equilibrium problem on Hadamard manifolds.National Natural Science Foundation of ChinaNatural Science Foundation of Guizhou Province (China)Dirección General de Enseñanza SuperiorJunta de AndalucíaNational Science Council of Taiwa

Remarks on multivalued nonexpansive mappings

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.Dirección General de Investigación Científica y TécnicaJunta de Andalucí

Best simultaneous approximation to totally bounded sequences in Banach spaces

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.National Natural Science Foundation of ChinaProgram for New Century Excellent Talent in UniversityDirección General de Investigación Científica y TécnicaJunta de Andalucí