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Journal of Function Spaces and Applications
Volume 2012, Article ID 724120, 11 pages
Research Article

Convexity and Proximinality in Banach Space

College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China

Received 9 March 2011; Accepted 9 November 2011

Academic Editor: Anna Kaminska

Copyright © 2012 Z. H. Zhang and C. Y. Liu. 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.


By the continuity of preduality map, we give some necessary and sufficient conditions of the strongly convex and very convex spaces, respectively. Using nearly strong convexity of 𝑋 , we give some equivalent conditions that every element in 𝑋 is strongly unique of order 𝑝 , bounded strongly unique of order 𝑝 , and locally strongly unique of order 𝑝 .