Dear Colleagues,

Fixed-point theory has wide applicability, but it was initially applied in order to prove the existence and, in some cases, uniqueness, of a special class of points satisfying a certain condition. Essentially, it represents the solution of an equation that can be of diverse nature: integral equations, differential equations, matrixial equations, etc. Such elements are known as “fixed points” because there must be an operator that associates these points to themselves.

The underlying space in which a fixed-point problem is posed must be provided with an abstract metric structure, that is, there must be a mapping that recalls the “distance” between two arbitrary points. At the beginning, only metric spaces were considered because they satisfied the key properties that guarantee the existence and uniqueness of fixed points: non-negativity, identity of indiscernibles, symmetry, and triangle inequality. However, along the years, many researchers have introduced a great variety of subtle changes that have generalized and extended the notion of “metric” in several ways. Today, it is usual to find investigations in the setting of extended real metrics, semimetrics, quasimetrics, pseudometrics, fuzzy metric spaces, probabilistic metric spaces, partial metric spaces, Branciari spaces, RS spaces, G-metric spaces, etc.

These modifications have highlighted, in recent years, the great importance of the notion of “metric” (or “distance”) which underlies the considered space. In several fields of study, it has become a key tool which deserves independent and theoretical study. For instance, the metric is essential in statistics in order to apply the minimum squares methodology, and also in the computer sciences, where the distance (or “similarity measure”) between two fuzzy objects is considered in many real-life problems as image detection or classification theory.

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 sciences.

Prof. Dr. Antonio Francisco Roldán López de Hierro
Guest Editor

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• Metric
• Distance
• Metric space
• Fixed point
• Regression analysis