Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PROXIMITY MAPS FOR CERTAIN SPACES

  • Published : 1997.05.01
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Abstract

Let K be a nonempty subset of a normed linear space X and let x $\in$ X. An element k$_0$ in K satisfying $\$\mid$$x - k$_0$$\$\mid$$ = d(x, K) := (equation omitted) $\$\mid$$x - k$\$\mid$$ is called a best approximation to x from K. For any x $\in$ X, the set of all best approximations to x from K is denoted by P$_K$(x) = {k $\in$ K : $\$\mid$$ x - k $\$\mid$$ = d(x, K)}. (omitted)

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