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Convex Functions of Legendre Type in General Banach Spaces

Borwein, Jonathan M. and Vanderwerff, Jon D. (2001) Convex Functions of Legendre Type in General Banach Spaces. Journal of Convex Analysis, 8 (2). pp. 569-581. ISSN 0944-6532

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      Abstract

      Convex functions of Legendre type are constructed on arbitrary open convex sets in Banach spaces that satisfy appropriate rotundity and smoothness conditions. A simple direct proof of universal barriers on arbitrary open convex sets or their closures in $\R^n$ is given.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: beta-differentiability, essentiall smooth, barrier function, Legendre function, strict convexity
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      46-xx Functional analysis > 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
      46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
      52-xx Convex and discrete geometry > 52Axx General convexity
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 13 Jan 2015 12:00
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/228

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