PROXIMITY MAPS FOR CERTAIN SPACES
Mun-Bae Lee, Sungho Park · Bulletin of the Korean Mathematical Society · 1997
Let K be a nonempty subset of a normed linear space X and let x X. An element k in K satisfying $\$x - k$\$ = d(x, K) := (equation omitted) $\$x - k$\$ is called a best approximation to x from K. For any x X, the set of all best approximations to x from K is denoted by P(x) = {k K : $\$ x - k $\$ = d(x, K)}. (omitted)