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Abstract and Applied Analysis
Volume 2014, Article ID 190203, 6 pages
http://dx.doi.org/10.1155/2014/190203
Research Article

Complex Convexity of Musielak-Orlicz Function Spaces Equipped with the -Amemiya Norm

Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Received 27 November 2013; Revised 5 April 2014; Accepted 13 April 2014; Published 8 May 2014

Academic Editor: Angelo Favini

Copyright © 2014 Lili Chen et al. 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

The complex convexity of Musielak-Orlicz function spaces equipped with the -Amemiya norm is mainly discussed. It is obtained that, for any Musielak-Orlicz function space equipped with the -Amemiya norm when , complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in above spaces are given. Criteria for complex strict convexity and complex midpoint locally uniform convexity of above spaces are also deduced.