Advances in Functional Analysis: Theoretical Results and Applications to Statistical Inference and Entropy

Dear Colleagues,

Functional analysis has its roots in the study of function spaces and in the formulation of properties of transformations of functions that define, for example, continuous or unitary operators between function spaces. The core of this branch is the study of vector spaces endowed with some kind of limit-related structure (topology, norm, inner product) and the linear functions defined in these spaces that suitably respect such structures. Functional analysis is helpful to study and solve both linear and nonlinear problems posed in a normed space that is no longer finite-dimensional, a situation that arises naturally in many concrete problems.

This fundamental area of mathematics is also used in many other domains. Among these areas, there has been a great deal of interest in applications to statistical inference and information measures, such as entropy and divergence.  This general topic of information measures (especially entropy and divergence measures) can be considered a broad scientific field that aims to develop methods and techniques for the inference and modelling of various phenomena in many domains.

In order to establish the degree of similarity and the degree of closeness between functions, distributions or populations, we can use the concept of distance. Thus, the distance is related to inferential statistics and modelling, with applications in reliability theory, survival analysis, actuarial science, multivariate analysis, regression analysis, portfolio optimization, etc. In this way, the significant importance of entropy and divergence measures makes this a topic of interest for researchers, scientists, engineers, computer experts, medical experts, data analysts and so on.

This Special Issue is focused on theoretical problems of functional analysis, but also on applications to the aforementioned fields. More specifically, it intends to cover recent developments in functional analysis and presents new theoretical issues that have not previously been presented in the literature, as well as solutions to important practical problems and case studies illustrating the application methodology. Original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

• Approximation theory;
• Equilibrium theory;
• Numerical functional analysis;
• Function spaces;
• Banach spaces;
• Variational inequalities;
• Multivariate analysis;
• Fixed-point theorems;
• Applied and theoretical statistics;
• Statistical inference;
• Information theory;
• Entropy;
• Divergence measures;
• Reliability theory;
• Survival analysis;
• Actuarial science.

We look forward to receiving your contributions.

Dr. Răzvan-Cornel Sfetcu
Prof. Dr. Vasile Preda
Guest Editors

Manuscript Submission Information

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• functional analysis
• statistical inference
• information theory
• entropy
• divergence measure
• survival analysis
• actuarial science