On Fermat Torricelli Problem in Frechet Spaces

On Fermat Torricelli Problem in Frechet Spaces

Author by Dr. Semiu Ayinde

Journal/Publisher: Journal Of Nepal Mathematical Society

Volume/Edition: 3

Language: English

Pages: 16 - 26

Abstract

We study 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 defined the topology of X as gauges. For a finite set A in X consisting of n distinct fixed points, the set of minimizers for the sum of distances from the point 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 the 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.


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