Artículo
A uniform betweenness property in metric spaces and its role in the quantitative analysis of the “Lion-man” game
Autor/es | Kohlenbach, Ulrich Wilhelm
López Acedo, Genaro Nicolae, Adriana |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2021-01-26 |
Fecha de depósito | 2023-04-14 |
Publicado en |
|
Resumen | We analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform betweenness property and use it in the study of a discrete ... We analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform betweenness property and use it in the study of a discrete lion and man game with an ε -capture criterion. In particular, we prove that in uniformly convex bounded domains the lion always wins and, using ideas stemming from proof mining, we extract a uniform rate of convergence for the successive distances between the lion and the man. As a byproduct of our analysis, we study the relation among different convexity properties in the setting of geodesic spaces. |
Cita | Kohlenbach, U.W., López Acedo, G. y Nicolae, A. (2021). A uniform betweenness property in metric spaces and its role in the quantitative analysis of the “Lion-man” game. Pacific Journal of Mathematics, 310 (1), 181-212. https://doi.org/10.2140/pjm.2021.310.181. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
pjm-v310-n1-p07-s.pdf | 446.8Kb | [PDF] | Este documento no está disponible a texto completo hasta el 2027-01-26 . Para más información póngase en contacto con idus@us.es. | |