Special Issue "Abstract Metric Spaces: Usefulness in Statistics and Fixed Point Theory"
Deadline for manuscript submissions: closed (31 March 2021).
Interests: fuzzy numbers; fuzzy decision making; fuzzy regression; aggregation functions; fixed point theory
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Four properties characterize the notion of “metric”: non-negativity, identity of indiscernibles, symmetry, and triangle inequality (which is, maybe, the most important inequality in Mathematics). By combining the power of these four axioms, many possible applications have been created in several fields of study, especially in Mathematics and Physics. After the pioneering works of Fréchet (1906) and Hausdorff (1914), a great variety of modifications of the original notion have been introduced in order to extend and adapt this definition to each respective researcher’s interest area: semimetrics, quasimetrics, pseudometrics, partial metric spaces, Branciari distances, RS-distances, G-metric spaces, etc.
Taking into account convergent and Cauchy sequences in metric spaces, it is well known that the notion of “metric” plays a key role in fixed point theory. However, such a concept is also essential in Statistics, because it can model natural random phenomena better than other algebraic tools. Thus, statistical metric spaces, Menger spaces, fuzzy metric spaces, intuitionistic metric spaces, etc. have been introduced. Furthermore, in regression analysis, errors are computed using some generalized metrics in order to compare observed and theoretical points.
This Special Issue is devoted (but not limited) to the wide range of applications of the notion of “metric” in all fields of study, including topics such as:
- Fixed point theory;
- Fuzzy distances;
- Generalized distances in abstract metrics spaces;
- Applications of metrics in Statistics;
- Use of metrics in regression analysis;
- Convergence analysis;
- Metrics in Computer Science.
Prof. Dr. Antonio Francisco Roldán López de Hierro
Manuscript Submission Information
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