Table of Contents Author Guidelines Submit a Manuscript
Journal of Mathematics
Volume 2017 (2017), Article ID 1073589, 9 pages
https://doi.org/10.1155/2017/1073589
Research Article

Orthogonal Symmetries and Reflections in Banach Spaces

University of Sharjah, Sharjah, UAE

Correspondence should be addressed to Ali Jaballah

Received 5 March 2017; Accepted 12 April 2017; Published 14 June 2017

Academic Editor: Ji Gao

Copyright © 2017 Ali Jaballah and Fathi B. Saidi. 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.

Linked References

  1. M. Sababheh and R. Khali, “Remotal points and a Krein-Milman type theorem,” Journal of Nonlinear and Convex Analysis. An International Journal, vol. 12, no. 1, pp. 5–15, 2011. View at Google Scholar · View at MathSciNet
  2. R. Khalil, “Orthogonality in Banach spaces,” Mathematics Journal of Toyama University, vol. 13, pp. 185–205, 1990. View at Google Scholar · View at MathSciNet
  3. C. Asci, “Differentiation theory over infinite–dimensional banach spaces,” Journal of Mathematics, vol. 2016, Article ID 2619087, 16 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  4. S. Wulede, W. Bai, and W. Bao, “A generalization of uniformly extremely convex Banach spaces,” Journal of Function Spaces, vol. 2016, Article ID 9161252, 6 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  5. I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York, NY, USA, 1970.
  6. F. Prus-Wis'niowski and W. H. Ruckle, “The Banach spaces ΛBV are non–reflexive,” Journal of Mathematical Analysis and Applications, vol. 389, no. 2, pp. 1394–1396, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. B. D. Roberts, “On the geometry of abstract vector spaces,” Tohoku Mathematical Journal, vol. 39, pp. 52–59, 1934. View at Google Scholar
  8. F. B. Saidi, “An extension of the notion of orthogonality to Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 267, no. 1, pp. 29–47, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. R. C. James, “Orthogonality in normed linear spaces,” Duke Mathematical Journal, vol. 12, pp. 291–302, 1945. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus