Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings

p(>= 2)-cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self-mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.

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.

In Vitro Surfactant and Perfluorocarbon Aerosol Deposition in a Neonatal Physical Model of the Upper Conducting Airways

Objective: Aerosol delivery holds potential to release surfactant or perfluorocarbon (PFC) to the lungs of neonates with respiratory distress syndrome with minimal airway manipulation. Nevertheless, lung deposition in neonates tends to be very low due to extremely low lung volumes, narrow airways and high respiratory rates. In the present study, the feasibility of enhancing lung deposition by intracorporeal delivery of aerosols was investigated using a physical model of neonatal conducting airways. Methods: The main characteristics of the surfactant and PFC aerosols produced by a nebulization system, including the distal air pressure and air flow rate, liquid flow rate and mass median aerodynamic diameter (MMAD), were measured at different driving pressures (4-7 bar). Then, a three-dimensional model of the upper conducting airways of a neonate was manufactured by rapid prototyping and a deposition study was conducted. Results: The nebulization system produced relatively large amounts of aerosol ranging between 0.3 +/- 0.0 ml/min for surfactant at a driving pressure of 4 bar, and 2.0 +/- 0.1 ml/min for distilled water (H(2)Od) at 6 bar, with MMADs between 2.61 +/- 0.1 mu m for PFD at 7 bar and 10.18 +/- 0.4 mu m for FC-75 at 6 bar. The deposition study showed that for surfactant and H(2)Od aerosols, the highest percentage of the aerosolized mass (similar to 65%) was collected beyond the third generation of branching in the airway model. The use of this delivery system in combination with continuous positive airway pressure set at 5 cmH(2)O only increased total airway pressure by 1.59 cmH(2)O at the highest driving pressure (7 bar). Conclusion: This aerosol generating system has the potential to deliver relatively large amounts of surfactant and PFC beyond the third generation of branching in a neonatal airway model with minimal alteration of pre-set respiratory support.

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.