The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces

XianFa Luo and JianYong Wang

Abstract and Applied Analysis, 2013, vol. 2013, 1-6

Abstract:

Let be a closed bounded convex subset of a real Banach space with as its interior and the Minkowski functional generated by the set . For a nonempty set in and , is called the generalized best approximation to from if for all . In this paper, we will give a distance formula under from a point to a closed hyperplane in determined by a nonzero continuous linear functional in and a real number α , a representation of the generalized metric projection onto , and investigate the continuity of this generalized metric projection, extending corresponding results for the case of norm.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:504076

DOI: 10.1155/2013/504076

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