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Journal of Function Spaces
Volume 2015, Article ID 478437, 7 pages
http://dx.doi.org/10.1155/2015/478437
Research Article

Generalized Projections on Closed Nonconvex Sets in Uniformly Convex and Uniformly Smooth Banach Spaces

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 6 April 2015; Accepted 30 May 2015

Academic Editor: Calogero Vetro

Copyright © 2015 Messaoud Bounkhel. 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. Y. I. Alber, “Generalized projection operators in Banach spaces: properties and applications,” Functional Differential Equations, vol. 1, no. 1, pp. 1–21, 1994. View at Google Scholar
  2. Y. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and appklications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Lecture Notes in Pure and Applied Mathematics, pp. 15–50, Dekker, New York, NY, USA, 1996. View at Google Scholar
  3. J. Li, “The generalized projection operator on reflexive Banach spaces and its applications,” Journal of Mathematical Analysis and Applications, vol. 306, no. 1, pp. 55–71, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  4. M. Bounkhel and R. Al-Yusof, “Proximal analysis in reflexive smooth Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 73, no. 7, pp. 1921–1939, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. M. Bounkhel and R. Al-Yusof, “First and second order convex sweeping processes in reflexive smooth Banach spaces,” Set-Valued and Variational Analysis, vol. 18, no. 2, pp. 151–182, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. J. Li, “On the existence of solutions of variational inequalities in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 295, no. 1, pp. 115–126, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Y. Alber and J. L. Li, “The connection between the metric and generalized projection operators in Banach spaces,” Acta Mathematica Sinica, English Series, vol. 23, no. 6, pp. 1109–1120, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. R. Deville, G. Godefroy, and V. Zizler, Smoothness and Renormings in Banach Spaces, vol. 64 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK, 1993. View at MathSciNet
  9. J. Diestel, Geometry of Banach Spaces—Selected Topics, Lecture Notes in Mathematics, Vol. 485, Springer, Berlin, Germany, 1975. View at MathSciNet
  10. W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, 2000. View at MathSciNet
  11. M. M. Vainberg, Variational Methods and Method of Monotone Operators in the Theory of Nonlinear Equations, John Wiley & Sons, New York, NY, USA, 1973.
  12. F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory, vol. 178 of Graduate Texts in Mathematics, Springer, Berlin, Germany, 1998. View at MathSciNet
  13. K. S. Lau, “Almost Chebyshev subsets in reflexive Banach spaces,” Indiana University Mathematics Journal, vol. 27, no. 5, pp. 791–795, 1978. View at Publisher · View at Google Scholar · View at MathSciNet