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UNIFORMLY CONVEX FUNCTIONS ON BANACH SPACES

Borwein, Jonathan M. and Guirao, Antonio J. and Vanderwerff, Jon D. (2009) UNIFORMLY CONVEX FUNCTIONS ON BANACH SPACES. Proceedings of the American Mathematical Society, 137 . pp. 1081-1091. ISSN 0002-9939

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    Abstract

    We study the connection between uniformly convex functions f : X -> R bounded above by ||x||^p, and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X -> R bounded above by ||.||2 if and only if X admits a norm with modulus of convexity of power type 2.

    Item Type: Article
    Additional Information: pubdom FALSE
    Subjects: 46-xx Functional analysis > 46Nxx Miscellaneous applications of functional analysis
    49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
    90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
    52-xx Convex and discrete geometry > 52Axx General convexity
    46-xx Functional analysis > 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
    Faculty: UNSPECIFIED
    Depositing User: lingyun ye
    Date Deposited: 16 Mar 2007
    Last Modified: 05 Jan 2015 16:25
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/340

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