Tangent cones, starshape and convexity

Borwein, Jonathan M. (1978) Tangent cones, starshape and convexity. International J. Math. and Math. Sci., 1 . pp. 459-477.

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In the last few years various infinite dimensional extensions to Krasnoselski's Theorem on starshaped sets [14] have been made. These began with a paper by Edelstein and Keener [8] and have culminated in the papers by Borwein, Edelstein and O'Brien [3] [4] by Edelstein, Keener and O'Brien [9] and finally by O'Brien [16]. Unrelatedly, Borwein and O'Brien [5] posed a question which arises in optimization [2] [11] of when a closed set is pseudoconvex at all its members. In this paper we show that these two questions can be handled simultaneously through a slight refinement of the powerful central result in [16] with attendant strengthening of the results in [5] [16]. This in turn leads to some interesting characterizations of convexity, starshape and of various functional conditions.

Item Type: Article
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 23 Feb 2015 14:36
Last Modified: 23 Feb 2015 14:36

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