| Autor: |
Jacek Graczyk, Nicolae Mihalache |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Journal of Mathematical Analysis and Applications. 507:125811 |
| ISSN: |
0022-247X |
| DOI: |
10.1016/j.jmaa.2021.125811 |
| Popis: |
We supply two optimal lower bounds for the solution of the analytical traveling salesman problem in terms of Jones' β-numbers. We prove a linear lower bound for the length of every connecting curve in the general case. The four corners Cantor set shows that the linear bound is attained. For connected compact sets, we prove an exponential lower bound for their length. The estimate is optimal by the work of Bishop and Jones [2] . Finally, we bridge connected and disconnected cases by taking into account multiplicity of orthogonal projections. Applications to other areas of mathematics are briefly discussed. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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