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.

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.

An investigation of imputation methods for discrete databases and multi-variate time series

When it comes to information sets in real life, often pieces of the whole set may not be available. This problem can find its origin in various reasons, describing therefore different patterns. In the literature, this problem is known as Missing Data. This issue can be fixed in various ways, from not taking into consideration incomplete observations, to guessing what those values originally were, or just ignoring the fact that some values are missing. The methods used to estimate missing data are called Imputation Methods. The work presented in this thesis has two main goals. The first one is to determine whether any kind of interactions exists between Missing Data, Imputation Methods and Supervised Classification algorithms, when they are applied together. For this first problem we consider a scenario in which the databases used are discrete, understanding discrete as that it is assumed that there is no relation between observations. These datasets underwent processes involving different combina- tions of the three components mentioned. The outcome showed that the missing data pattern strongly influences the outcome produced by a classifier. Also, in some of the cases, the complex imputation techniques investigated in the thesis were able to obtain better results than simple ones. The second goal of this work is to propose a new imputation strategy, but this time we constrain the specifications of the previous problem to a special kind of datasets, the multivariate Time Series. We designed new imputation techniques for this particular domain, and combined them with some of the contrasted strategies tested in the pre- vious chapter of this thesis. The time series also were subjected to processes involving missing data and imputation to finally propose an overall better imputation method. In the final chapter of this work, a real-world example is presented, describing a wa- ter quality prediction problem. The databases that characterized this problem had their own original latent values, which provides a real-world benchmark to test the algorithms developed in this thesis.