Bulletin of the Belgian Mathematical Society - Simon Stevin

Optimization through dense sets

C. R. Jayanarayanan and T. S. S. R. K. Rao

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper, we study two optimization problems where solutions on a dense set yield global solution. We study these problems for spaces of Bochner integrable functions and for spaces of continuous functions. The first one deals with expressing the length of a vector as a sum of the distance to a best approximation and minimal best approximation and the second one relates to approximating a subsequence of a minimizing sequence with a sequence of proximinal vectors.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 4 (2016), 583-594.

First available in Project Euclid: 6 December 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
Secondary: 46E40: Spaces of vector- and operator-valued functions 46B20: Geometry and structure of normed linear spaces 41A50: Best approximation, Chebyshev systems

Proximinality strong proximinality space of Bochner integrable functions space of continuous functions


Jayanarayanan, C. R.; Rao, T. S. S. R. K. Optimization through dense sets. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 4, 583--594. https://projecteuclid.org/euclid.bbms/1480993589

Export citation