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.

Le courant de Lomonosov dans le fond du Golfe de Guinée en mai 1973

A cruise of the R. V. Capricorne in May 1973, in inner part of the gulf of Guinea, allowed the authors to identify the main part of the Atlantic circulation at the longitude of 5 degrees E, between 4 degrees N and 4 degrees S. It gave new data on the termination of the equatorial undercurrent. At the equator, under the westward south equatorial current flows the Atlantic equatorial undercurrent with a maximum eastward velocity of 90 cm/sec at 30 m depth linked to a salinity maximum higher than 36.20 ppt. Below the equatorial undercurrent, about 80-100 m depth, flows a westward current with a velocity as high as 30 cm/sec. At 4 degrees S, the south equatorial countercurrent is well delineated by a high salinity core (more than 36.10 ppt) at 30 m depth with an eastward velocity core of 40 cm/sec. On the contrary, near 3 degrees 30N, a high salinity core (36.10 ppt) flows westwards with a speed of 40 cm/sec at 40 m depth: it is the "return flow" of the undercurrent (Hisard and Moliere 1974). At 4 degrees N the Guinea current carries eastwards surface salinities of 34.50 ppt at 40 cm/sec. Off Cape Lopez (0 degrees 35'S-8 degrees 42'E) the high salinity core of the undercurrent becomes wider near the shore. It is 25m wide offshore, and 70 m wide near the cape. A part of undercurrent water extends northwards, then flows westwards with the subsurface westward circulation in the inner part of the Gulf of Guinea. Another part flows south-southwestwards in a high salinity tongue along the African coast to 4 degrees S. South-west of Cape Lopez, the trades divergence contributes to an upwelling of cold and high salinity water; this water increases at the Cape Lopez front.

An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.

Algorithm for identification in the v-gap metric

This paper suggests a method for identification in the v-gap metric. For a finite number of frequency response samples, a problem for identification in the v-gap metric is formulated and an approximate solution is described. It uses an iterative technique for obtaining an L2-gap approximation. Each stage of the iteration involves solving an LMI optimisation. Given a known stabilising controller and the L2-gap approximation, it is shown how to derive a v-gap approximation.