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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 746309, 9 pages
http://dx.doi.org/10.1155/2014/746309
Research Article

-Uniform Convexity and -Uniform Smoothness of Absolute Normalized Norms on

Department of Basic Sciences, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan

Received 19 September 2013; Accepted 15 November 2013; Published 16 February 2014

Academic Editor: Henryk Hudzik

Copyright © 2014 Tomonari Suzuki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first prove characterizations of -uniform convexity and -uniform smoothness. We next give a formulation on absolute normalized norms on . Using these, we present some examples of Banach spaces. One of them is a uniformly convex Banach space which is not -uniformly convex.