Some questions in metric fixed point theory, by A. W. Kirk, revisited

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

Aplicaciones de las categorías de Baire a la existencia de solución de una ecuación diferencial en un espacio de Banach

Revista. Tomo LXXV. Cuaderno Primero.. Artículo 20

Matrices de Hadamard

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 de errores y corrección de códigos y finalmente problemas más modernos enmarcados en la Teoría Geométrica de los espacios de Banach

Generic existence of a nonempty compact set of fixed points

AbstractLet X be a complete metric space, M a set of continuous mappings from X into itself, endowed with a metric topology finer than the compact-open topology. Assuming that there exists a dense subset N contained in M such that for every mapping T in N the set {x ϵ X: Tx = x} is nonempty, it is proved that most mappings (in the Baire category sense) in M do have a nonempty compact set of fixed points. Some applications to α-nonexpansive operators, semiaccretive operators and differential equations in Banach spaces are derived

Some renormings with the stable fixed point property

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 general nonseparable, Banach space with an extended unconditional basis can be renormed to satisfy the w-FPP with the same stability constant.Ministerio de Ciencia e InnovaciónJunta de AndalucíaFaculty of Science, Chiangmai Universit

Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

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 Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.Dirección General de Enseñanza SuperiorJunta de Andalucí

Asymptotic centers and fixed points for multivalued nonexpansive mappings

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 uniform convexity, Abstr. Appl. Anal. 2003:6 (2003), 375–386 and solves an open problem appearing in Xu, H.K., Metric fixed point theory for multivalued mappings, Dissertationes Math. (Rozprawy Mat.) 389 (2000), 39 pp.Dirección General de Enseñanza SuperiorJunta de Andalucí

Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

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 point for asymptotically nonexpansive mappings can be extended to obtain a common fixed point for a commuting family of mappings. We also derive some results about convergence of iterates.Dirección General de Investigación Científica y TécnicaJunta de Andalucí

Measures of noncompactness in modular spaces and fixed point theorems for multivalued nonexpansive mappings

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 for multivalued nonexpansive mappings in modular spaces