Josefa Marín

On the Bitopological Extension of the Bing Metrization Theorem

Based on a Junnilas paracompactness characterization we give a definition of pairwise paracompact space which permits us to prove that a bitopological space is quasi-metrizable if, and only if, it is a pairwise developable and pairwise paracompact space. An easy consequence of this result is the biquasi-metric form of the Morita metrization theorem. We also give some results on open mappings and strong quasi-metrics.

Weakly contractive multivalued maps and w- distances on complete quasi-metric spaces

We obtain versions of the Boyd and Wong fixed point theorem and of the Matkowski fixed point theorem for multivalued maps and w-distances on complete quasi-metric spaces. Our results generalize, in several directions, some well-known fixed point theorems.

Generalized Contractive Set-Valued Maps on Complete Preordered Quasi-Metric Spaces

By using a suitable modification of the notion of a -distance we obtain some fixed point results for generalized contractive set-valued maps on complete preordered quasi-metric spaces. We also show that several distinguished examples of non-metrizable quasi-metric spaces and of cones of asymmetric normed spaces admit -distances of this type. Our results extend and generalize some well-known fixed point theorems.

A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces

AbstractWe obtain a fixed point theorem for generalized contractions on complete quasi-metric spaces, which involves w-distances and functions of Meir-Keeler and Jachymski type. Our result generalizes in various directions the celebrated fixed point theorems of Boyd and Wong, and Matkowski. Some illustrative examples are also given. MSC:47H10, 54H25, 54E50.

Functions on Quasimetric Spaces and Fixed Points for Multivalued Maps

We discuss several properties of -functions in the sense of Al-Homidan et al.. In particular, we prove that the partial metric induced by any weighted quasipseudometric space is a -function and show that both the Sorgenfrey line and the Kofner plane provide significant examples of quasimetric spaces for which the associated supremum metric is a -function. In this context we also obtain some fixed point results for multivalued maps by using Bianchini-Grandolfi gauge functions.The authors thank one of the reviewers for suggesting the inclusion of a concrete example to which Theorem 3.3 applies. They acknowledge the support of the Spanish Ministry of Science and Innovation, Grant no. MTM2009-12872-C02-01.

A Caristi fixed point theorem for complete quasi-metric spaces by using mw-distances

In this paper we give a quasi-metric version of Caristi’s fixed point theorem by using mw-distances. Our theorem generalizes a recent result obtained by Karapinar and Romaguera in [7]. Mathematics Subject Classification (2010): 47H10, 54H25, 54E50,

PHYSICAL-MATHEMATICAL CONCEPTS IN A SIMPLIFIED STUDY OF THE PROTOCOL OF THE LAUNCH OF A ROCKET TO PUT A SATELLITE INTO ORBIT

The achievement of a comprehensive education of the students to provide a global knowledge that allows them to make appropriate decisions in the framework of their future work is one of the most important challenges of the Engineering degrees, especially in basic subjects as Physics or Mathematics. In this sense, a great effort has to be done by the teachers of the first year where the subjects are generally quite abstract and, as a consequence, the motivation of the students is hard to attain. Several are the conditions to obtain this goal successfully: First, a correct cross-coordination and a well-designed teaching of the basis subjects to avoid undesirable repetition of some concepts under different point of view and to show the basic knowledge as a uniform conceptual body ready to be applied to real situations. Second, the need to make attractive the study of these basic and abstract subjects by proposing the resolution of real problems related with the goals of each particular Degree, and adapted to the knowledge of the student of the first level. These problems have to be solved involving different branch of the basic subjects as Physics or Mathematics. In this paper we present a real project related to the professional skills of the Geomatic and Topography Degree, adapted for the first level, and involving three core subjects namely, Algebra, Calculus and Mechanics. The approach of this real project, proposed as an interdisciplinary practice, is related with the path followed by a rocket that puts a satellite in orbit. In real situations, sixteen are the steps of the protocol to achieve this goal, from the takeoff of the rocket to its entrance on the final elliptic orbit. To adapt this complicated protocol to our purposes, we have simplified the steps considering finally only four: (i) the takeoff of the rocket; (ii) the change of the upright path at a predetermined height from the ground to approach to the elliptical orbit; (iii) the link between the rise of the rocket and its placing in elliptical orbit; (iv) the putting into the elliptical orbit itself. Analysis of classic geometric figures as the conics, with their different forms of representation, becomes necessary to be able to develop this practice, since they adapt to the forms described by orbits of the satellites. Modeling makes it necessary to use different reference systems and their relationship between them. In addition, the simplified study of the satellite position vector in its different phases provides fundamental data such as speed, acceleration or balance of forces, related with the subjects of Dynamic or Kinematics, and where the concept of derivative plays a fundamental role. A later detailed study on the motion of the satellite would lead to propose systems of differential equations that relate the elements studied and whose complexity requires numerical methods for their resolution.

Submetrizable Yoneda complete structures for a metric dcpo

We show that every metric dcpo admits a quantitative computational model defined by a submetrizable Yoneda complete quasi-metric dcpo that preserves the main computational interpretations derived from the order structure of the metric dcpo and allows us to distinguish between comparable and non comparable objects. The Baire metric on the domain of words and the complexity space are typical examples where our approach nicely works.

Open image in new window -Functions on Quasimetric Spaces and Fixed Points for Multivalued Maps

We discuss several properties of -functions in the sense of Al-Homidan et al.. In particular, we prove that the partial metric induced by any weighted quasipseudometric space is a -function and show that both the Sorgenfrey line and the Kofner plane provide significant examples of quasimetric spaces for which the associated supremum metric is a -function. In this context we also obtain some fixed point results for multivalued maps by using Bianchini-Grandolfi gauge functions.The authors thank one of the reviewers for suggesting the inclusion of a concrete example to which Theorem 3.3 applies. They acknowledge the support of the Spanish Ministry of Science and Innovation, Grant no. MTM2009-12872-C02-01.