Characterization of \(\varepsilon\)-nearest points in spaces with asymmetric seminorm

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Costică Mustăţa

Abstract

In this note we are concerned with the characterization of the elements of \(\varepsilon\)-best approximation (\(\varepsilon\)-nearest points) in a subspace \(Y\) of space \(X\) with asymmetric seminorm. For this we use functionals in the asymmetric dual \(X^{b}\) defined and studied in some recent papers [1], [2], [5].

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Keywords
asymmetric seminormed spaces; \(\varepsilon\)-nearest points; characterization
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