Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2008, Article ID 135873, 5 pages
http://dx.doi.org/10.1155/2008/135873
Research Article

Modulus of Convexity, the Coeffcient , and Normal Structure in Banach Spaces

1Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China
2Department of Mathematics, Luoyang Normal University, Luoyang 471022, China

Received 7 April 2008; Accepted 27 May 2008

Academic Editor: William A. Kirk

Copyright © 2008 Hongwei Jiao 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.

Linked References

  1. S. Dhompongsa, A. Kaewkhao, and S. Tasena, “On a generalized James constant,” Journal of Mathematical Analysis and Applications, vol. 285, no. 2, pp. 419–435, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. Gao, “Modulus of convexity in Banach spaces,” Applied Mathematics Letters, vol. 16, no. 3, pp. 273–278, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Jiménez-Melado, E. Llorens-Fuster, and S. Saejung, “The von Neumann-Jordan constant, weak orthogonality and normal structure in Banach spaces,” Proceedings of the American Mathematical Society, vol. 134, no. 2, pp. 355–364, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. E. M. Mazcuñán-Navarro, “Banach space properties sufficient for normal structure,” Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 197–218, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Saejung, “The characteristic of convexity of a Banach space and normal structure,” Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 123–129, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. Goebel, “Convexivity of balls and fixed-point theorems for mappings with nonexpansive square,” Compositio Mathematica, vol. 22, pp. 269–274, 1970. View at Google Scholar · View at MathSciNet
  7. J. A. Clarkson, “Uniformly convex spaces,” Transactions of the American Mathematical Society, vol. 40, no. 3, pp. 396–414, 1936. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Prus, “Some estimates for the normal structure coefficient in Banach spaces,” Rendiconti del Circolo Matematico di Palermo, vol. 40, no. 1, pp. 128–135, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. Domínguez Benavides, “A geometrical coefficient implying the fixed point property and stability results,” Houston Journal of Mathematics, vol. 22, no. 4, pp. 835–849, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990. View at Zentralblatt MATH · View at MathSciNet
  11. M. Kato, L. Maligranda, and Y. Takahashi, “On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces,” Studia Mathematica, vol. 144, no. 3, pp. 275–295, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet