STABILITY OF CLOSEDNESS OF CONVEX CONES UNDER LINEAR MAPPINGS II

Authors

  • J. Borwein CENTRE FOR COMPUTER ASSISTED MATHEMATICS AND ITS APPLICATIONS (CARMA), UNIVERSITY OF NEWCASTLE,CALLAGHAN, NSW 2308, AUSTRALIA.
  • W. Moors DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF AUCKLAND, PRIVATE BAG 92019, AUCKLAND, NEW ZEALAND.

Abstract

In this paper we revisit the question of when the continuous linear image of a fixed closed convex cone $K$ is closed. Specifically, we improve the main result of [3] by showing that for all, except for at most a $\sigma$-porous set, of the linear mappings $T$ from $R^n$ into $R^m$, not only is $T(K)$ closed, but there is also a neighbourhood around $T$ whose members also preserve the closedness of $K$.

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Published

2010-03-31

How to Cite

Borwein, J., & Moors, W. (2010). STABILITY OF CLOSEDNESS OF CONVEX CONES UNDER LINEAR MAPPINGS II. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 1(1), 1-7. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/5

Issue

Section

Research Article