Abstract
We develop a theory of simultaneous metric projection in a normed linear space $X$ and present various characterizations of simultaneous metric projection onto closed convex sets in terms of the elements of $X^{\ast}$. Also, we characterize the elements of simultaneous metric projection onto closed convex sets in terms of extreme points of the closed unit ball $B_{X^{\ast}}.$ Finally, as an application, we give various characterizations of simultaneous metric projection onto subspaces of the Banach space $C(Q,Y).$
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