On Fermat-Torricelli Problem in Frechet Spaces
| Autor: | S.A. Ayinde, Gboyega A. Adebayo, James A. Oguntuase, Idowu Ademola Osinuga |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Nepal Mathematical Society. 3:16-26 |
| ISSN: | 2616-0161 2616-0153 |
| DOI: | 10.3126/jnms.v3i2.33956 |
| Popis: | We study the Fermat-Torricelli problem (FTP) for Frechet space X, where X is considered as an inverse limit of projective system of Banach spaces. The FTP is defined by using fixed countable collection of continuous seminorms that defines the topology of X as gauges. For a finite set A in X consisting of n distinct and fixed points, the set of minimizers for the sum of distances from the points in A to a variable point is considered. In particular, for the case of collinear points in X, we prove the existence of the set of minimizers for FTP in X and for the case of non collinear points, existence and uniqueness of the set of minimizers are shown for reflexive space X as a result of strict convexity of the space. |
| Databáze: | OpenAIRE |
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