Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2010 (2010), Article ID 102462, 14 pages
http://dx.doi.org/10.1155/2010/102462
Research Article

On - and -Convexity of Banach Spaces

Department of Mathematics, Center for Mathematical Reserch, A.C., Apdo. Postal 402, 36000 Guanajuato, GTO, Mexico

Received 25 June 2010; Accepted 18 August 2010

Academic Editor: Stevo Stevic

Copyright © 2010 Omar Muñiz-Pérez. 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. C. A. Kottman, “Packing and reflexivity in Banach spaces,” Transactions of the American Mathematical Society, vol. 150, pp. 565–576, 1970. View at Google Scholar · View at Zentralblatt MATH
  2. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, Mass, USA, 1990. View at Publisher · View at Google Scholar
  3. W. L. Bynum, “A class of spaces lacking normal structure,” Compositio Mathematica, vol. 25, pp. 233–236, 1972. View at Google Scholar · View at Zentralblatt MATH
  4. A. G. Aksoy and M. A. Khamsi, Nonstandard Methods in Fixed Point Theory, Universitext, Springer, New York, NY, USA, 1990.
  5. S. V. R. Naidu and K. P. R. Sastry, “Convexity conditions in normed linear spaces,” Journal für die Reine und Angewandte Mathematik, vol. 297, pp. 35–53, 1978. View at Google Scholar · View at Zentralblatt MATH
  6. O. Muñiz-Pérez, Convexidad en espacios de Banach y permanencia bajo ψ-sumas directas, Ph.D. thesis, CIMAT, México, 2010.
  7. K. S. Lau, “Best approximation by closed sets in Banach spaces,” Journal of Approximation Theory, vol. 23, no. 1, pp. 29–36, 1978. View at Google Scholar · View at Zentralblatt MATH
  8. J. Gao, “Normal structure and modulus of U-convexity in Banach spaces,” in Function Spaces, Differential Operators and Nonlinear Analysis, pp. 195–199, Prometheus, Prague, Czech Republic, 1996. View at Google Scholar
  9. E. M. Mazcuñán-Navarro, “On the modulus of U-convexity of Ji Gao,” Abstract and Applied Analysis, vol. 2003, no. 1, pp. 49–54, 2003. View at Publisher · View at Google Scholar
  10. S. Saejung, “On the modulus of U-convexity,” Abstract and Applied Analysis, vol. 2005, no. 1, pp. 59–66, 2005. View at Publisher · View at Google Scholar
  11. L. Maligranda, “Some remarks on the triangle inequality for norms,” Banach Journal of Mathematical Analysis, vol. 2, no. 2, pp. 31–41, 2008. View at Google Scholar · View at Zentralblatt MATH
  12. S. Dhompongsa, A. Kaewkhao, and S. Saejung, “Uniform smoothness and U-convexity of ψ-direct sums,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 2, pp. 327–338, 2005. View at Google Scholar
  13. R. R. Phelps, “Uniqueness of Hahn-Banach extensions and unique best approximation,” Transactions of the American Mathematical Society, vol. 95, pp. 238–255, 1960. View at Google Scholar · View at Zentralblatt MATH
  14. K.-S. Saito, M. Kato, and Y. Takahashi, “Absolute norms on 2,” Journal of Mathematical Analysis and Applications, vol. 252, no. 2, pp. 879–905, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Y. Takahashi, M. Kato, and K.-S. Saito, “Strict convexity of absolute norms on 2 and direct sums of Banach spaces,” Journal of Inequalities and Applications, vol. 7, no. 2, pp. 179–186, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. O. Muñiz-Pérez, “Convexity conditions of ψ-direct sums,” preprint.
  17. J. M. Ayerbe Toledano, T. Domínguez Benavídez, and G. López Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhäuser, Basel, Switzerland, 1997.