TY - JOUR
AU - Osinuga, I.A.
AU - Ayinde, S.A.
AU - Oguntuase, J.A.
AU - Adebayo, G.A.
PY - 2020/12/30
Y2 - 2022/08/11
TI - On Fermat-Torricelli Problem in Frechet Spaces
JF - Journal of Nepal Mathematical Society
JA - J. Nep. Math. Soc.
VL - 3
IS - 2
SE - Articles
DO - 10.3126/jnms.v3i2.33956
UR - https://www.nepjol.info/index.php/jnms/article/view/33956
SP - 16-26
AB - <p>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.</p>
ER -