On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Baserriaren sakabanaketa, bertan bizi den zaharraren ostopoa: lezo eta Usurbilgo adibideak

[ES] El medio rural se enfrenta a un grado de envejecimiento muy elevado, mayor aún que el de las ciudades. Las necesidades en materia de atención social se incrementan en estos espacios, situación agravada por la falta de servicios sociales en sus municipios y por su lejanía. Incluso las comunidades rurales próximas a núcleos urbanos de entidad se enfrentan a este problema. En el caso en estudio recogemos la realidad social del medio rural próximo a San Sebastián, caracterizado por un habitante envejecido, un alto grado de dependencia agravado por residir en un hábitat disperso y un problema cuya asunción se atribuye a la mujer de la familia

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Skate elektriko baten gauzatzea, hautabideak eta diseinua.

[EU]Lan honetan hutsetik hasita skate motorizatu baten diseinu bat egin da, Industria Teknologian Ingeniaritzako Graduan eskuratutako jakintzak erabiliz. Skatea gazteengan oso erabilia den garraiobide bat da aisia dela-eta, eta sinpletasuna eta ekonomia kontuan hartuta, aisia eta ingurugiroarekiko konpromisoa nahasten dira diseinu honekin. Lanak bide argi bat dauka: hasieran merkatuaren egoera aztertzen da, gero diseinu posible batzuk proposatu ahal izateko, eta hortik aukera bat jorratu ahal izateko. Hortaz, prozesua hasieratik hasita, egitura hau izango du lanak: Hasteko, skate motorizatuen merkatuko egoera zein den aztertzen da, ondoren eta helburuak zeintzuk diren kontutan izanda, diseinu posible batzuk proposatu ahal izateko, alternatiben analisien atalean ageri direnak. Proposamen horiek aztertu egiten dira, alde on eta txarrak desberdinduz eta horietako soluzio bat aukeratuz. Aukeratutako diseinuaren CAD modelo bat eraikitzen da, ondoren egoera fisikoa matematikoki modelizatzeko eta beharrezko kalkuluak egin ahal izateko, metodologia atalean eta eranskinetan ageri direnak, hala nola, azelerazio jakin bat lortzeko behar den potentzia, transmisioan beharrezkoak diren kalkuluak kokatu beharreko elementuak zeintzuk diren erabaki ahal izateko, etab. Bide honetan, jorraturiko diseinuaz gain beste diseinu optimizatu eta konplexuago bat proposatzen da, ikerketa bidea zabalik duena, enpresa mundura gehiago zuzendua. Azkenik, lana burutzeko bete behar izan diren ataza bakoitzaren deskribapena eta iraupena, aurrekontua eta gastu aitorpena, arriskuen analisia eta proiektu honetatik atera ditugun ondorioak ematen dira.

Propuesta de intervención de actividad física contra el sedentarismo en lonjas juveniles del barrio bilbaino de Zorrotza

[ES] Con el presente estudio descriptivo se pretende obtener los siguientes objetivos: reunir la mayor bibliografía posible sobre las lonjas juveniles. Conocer estos tipos de espacios y qué actividades son las que se realizan en ellos. Tomando como punto de partida la observación de una lonja ubicada en el barrio Bilbaíno de Zorroza, se analizarán los comportamientos que se dan en estos espacios. Además se pretende ofrecer terminología sobre la juventud de hoy en día y las actividades de ocio en las que participan. Los estudios previos destacan un elevado consumo de drogas seguido de hábitos sedentarios. Al mismo tiempo, se presenta una propuesta de intervención en estos espacios y poder así ofrecer alternativas de ocio contra el sedentarismo a medio y largo plazo. Se espera de este trabajo que nos ofrezca más información sobre las actividades que se realizan en las lonjas juveniles y el tipo de drogas que más se consumen ellas, así como la frecuencia con la que se consumen.

Low‑cost origami fabrication of 3D self‑aligned hybrid microfluidic structures

[EN] 3D microfluidic device fabrication methods are normally quite expensive and tedious. In this paper, we present an easy and cheap alternative wherein thin cyclic olefin polymer (COP) sheets and pressure sensitive adhesive(PSA) were used to fabricate hybrid 3D microfluidic structures, by the Origami technique, which enables the fabrication of microfluidic devices without the need of any alignment tool. The COP and PSA layers were both cut simultaneously using a portable, low-cost plotter allowing for rapid prototyping of a large variety of designs in a single production step. The devices were then manually assembled using the Origami technique by simply combining COP and PSA layers and mild pressure. This fast fabrication method was applied, as proof of concept, to the generation of a micromixer with a 3D-stepped serpentine design made of ten layers in less than 8 min. Moreover, the micromixer was characterized as a function of its pressure failure, achieving pressures of up to 1000 mbar. This fabrication method is readily accessible across a large range of potential end users, such as educational agencies (schools,universities), low-income/developing world research and industry or any laboratory without access to clean room facilities, enabling the fabrication of robust, reproducible microfluidic devices.