Bilkent Üniversitesi Matematik Bölümü Seminerleri
Existence and Uniqueness of Best Approximations in Metric Spaces
Ahmet Nihat Şimşek
Bilkent University, Türkiye
In a metric space $X$ a best approximation of a given point $P$ to a set $M$ is the point $Q$ in $M$ that is nearest to $P$. But such a point may or may not exist and there may be several of them. We discuss existence and uniqueness of best approximations. Also we give some information about problem of convexity of Chebyshev sets.
