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Uniformly convex functions on Banach Spaces

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journal contribution
posted on 2025-05-11, 22:34 authored by Jonathan M. Borwein, A. J. Guirao, P. Hájek, J. Vanderwerff
Given a Banach space (Χ,∥ · ∥), we study the connection between uniformly convex functions f : Χ → R bounded above by ∥ · ∥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 : Χ → ℝ bounded above by ∥ · ∥² if and only if Χ admits an equivalent norm with modulus of convexity of power type 2.

History

Journal title

Proceedings of the American Mathematical Society

Volume

137

Issue

3

Pagination

1081-1091

Publisher

American Mathematical Society

Language

  • en, English

College/Research Centre

Faculty of Science and Information Technology

School

School of Mathematical and Physical Sciences

Rights statement

First published in the Proceedings of the American Mathematical Society in 2009, published by the American Mathematical Society.

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