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].
Publisher
Academia Romana Filiala Cluj
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis,Mathematics (miscellaneous)
Reference18 articles.
1. Borodin, P. A., The Banach-Mazur theorem for spaces with an asymmetric norm and its applications in convex analysis, Mat. Zametki, 69, no. 3, pp. 193-217, 2001.
2. De Blasi, F. S. and Myjak, J., On a generalized best approximation problem, J. Approx. Theory, 94, no. 1, pp. 54-72, 1998, https://doi.org/10.1006/jath.1998.3177
3. Cobzas, S. and Mustata, C., Extension of bounded linear functionals and best approximation in spaces with asymmetric norm, Rev. Anal. Numér. Théor. Approx., 33, no. 1, pp. 39-50, 2004, http://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art5
4. Cobzas, S., Separation of convex sets and best approximation in spaces with asymmetric norm, Quaest. Math., 27, pp. 1-22, (275-296), 2004, https://doi.org/10.2989/16073600409486100
5. Garcia-Raffi, L. M., Romaguera S. and Sánchez-Pérez, E. A., The dual space of an asymmetric normed linear space, Quaest. Math., 26, no. 1, pp. 83-96, 2003, https://doi.org/10.2989/16073600309486046