On Fermat-Torricelli Problem in Frechet Spaces

Authors

  • I.A. Osinuga Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
  • S.A. Ayinde Babcock University, Ilishan-Remo, Ogun State, Nigeria
  • J.A. Oguntuase Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
  • G.A. Adebayo Federal University of Agriculture, Abeokuta, Ogun State, Nigeria

DOI:

https://doi.org/10.3126/jnms.v3i2.33956

Keywords:

Reflexive Frechet spaces, Fermat-Torricelli problem, Strict convexity, Set of minimizers

Abstract

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.

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Author Biographies

I.A. Osinuga, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria

Department of Mathematics

S.A. Ayinde, Babcock University, Ilishan-Remo, Ogun State, Nigeria

Basic Sciences Department

J.A. Oguntuase, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria

Department of Mathematics

G.A. Adebayo, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria

Department of Physics

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Published

2020-12-30

How to Cite

Osinuga, I., Ayinde, S., Oguntuase, J., & Adebayo, G. (2020). On Fermat-Torricelli Problem in Frechet Spaces. Journal of Nepal Mathematical Society, 3(2), 16–26. https://doi.org/10.3126/jnms.v3i2.33956

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Articles