Abstract
The present paper is concerned with the characterization of the elements of best approximation in a subspace \(Y\) of a space with asymmetric norm, in terms of some linear functionals vanishing on \(Y\). The approach is based on some extension results, proved in Section 3, for bounded linear functionals on such spaces. Also, the well known formula for the distance to a hyperplane in a normed space is extended to the nonsymmetric case.
Authors
Ştefan Cobzaş
Babes-Bolyai University
Costica Mustata
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania
Keywords
Spaces with asymmetric norm; best approximation; Hahn-Banach theorem; characterization of best approximation.
Paper coordinates
C. Mustăţa and Şt. Cobzaş, Extension of bounded linear functionals and best approximation in space with asymmetric norm, Rev. Anal. Numer. Theor. Approx.. 33 (2004) no. 1, 39-50.
About this paper
Journal
Revue d’Analyse Numer. Theor. Approx.
Publisher Name
Publishing Romanian Academy
Print ISSN
2457-6794
Online ISSN
2501-059X
google scholar link
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