Monotone path-connected sets in geometric approximation theory and their applications
Alexey Rostislavovich Alimov, Игорь Германович Царьков · Mathematics and Theoretical Computer Science · 2024
Monotone sets have been quite actively studied in recent years in geometric approximation theory. The concept of monotone path-connected sets has proved especially useful. The purpose of the present paper is to give a short but comprehensive survey on this topic; we also illustrate relations with key properties of approximating sets, of which we consider characterizations of best approximants, and properties of uniqueness and stability.