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Journal of Function Spaces
Volume 2014 (2014), Article ID 634842, 4 pages
Research Article

Circle-Uniqueness of Pythagorean Orthogonality in Normed Linear Spaces

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

Received 30 December 2013; Revised 5 February 2014; Accepted 7 February 2014; Published 11 March 2014

Academic Editor: Yongqiang Fu

Copyright © 2014 Senlin Wu 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.


We introduce the circle-uniqueness of Pythagorean orthogonality in normed linear spaces and show that Pythagorean orthogonality is circle-unique if and only if the underlying space is strictly convex. Further related results providing more detailed relations between circle-uniqueness of Pythagorean orthogonality and the shape of the unit sphere are also presented.