Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2009, Article ID 243604, 11 pages
http://dx.doi.org/10.1155/2009/243604
Research Article

Porosity of Convex Nowhere Dense Subsets of Normed Linear Spaces

1Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland
2Institute of Mathematics of the Technical University of Łódź, Wólczańska 215, 93-005, Łódź, Poland

Received 9 June 2009; Revised 24 September 2009; Accepted 29 November 2009

Academic Editor: Simeon Reich

Copyright © 2009 Filip Strobin. 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. F. S. De Blasi and J. Myjak, “Sur la porosité de l'ensemble des contractions sans point fixe,” Comptes Rendus de l'Académie des Sciences Paris, vol. 308, no. 2, pp. 51–54, 1989. View at Google Scholar · View at MathSciNet
  2. S. Reich, “Genericity and porosity in nonlinear analysis and optimization,” in Proceedings of the Computer Methods and Systems (CMS '05), pp. 9––15, Cracow, Poland, November 2005, ESI preprint 1756.
  3. L. Zajíček, “Porosity and σ-porosity,” Real Analysis Exchange, vol. 13, no. 2, pp. 314–350, 1987-1988. View at Google Scholar · View at MathSciNet
  4. L. Zajíček, “On σ-porous sets in abstract spaces,” Abstract and Applied Analysis, vol. 2005, no. 5, pp. 509–534, 2005, Proceedings of the International Workshop on Small Sets in Analysis, E. Matoušková, S. Reich and A. Zaslavski, Eds., Hindawi Publishing Corporation, New York, NY, USA. View at Publisher · View at Google Scholar · View at MathSciNet
  5. V. Olevskii, “A note on the Banach-Steinhaus theorem,” Real Analysis Exchange, vol. 17, no. 1, pp. 399–401, 1991-1992. View at Google Scholar · View at MathSciNet
  6. F. Strobin, “A comparison of two notions of porosity,” Commentationes Mathematicae, vol. 48, no. 2, pp. 209–219, 2008. View at Google Scholar · View at MathSciNet
  7. D. Preiss and L. Zajíček, “Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions,” Rendiconti del Circolo Matematico di Palermo, Serie II, no. 3, supplement, pp. 219–223, 1984. View at Google Scholar · View at MathSciNet
  8. W. Rudin, Functional Analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, New York, NY, USA, 2nd edition, 1991. View at MathSciNet
  9. J. Duda, “On the size of the set of points where the metric projection exists,” Israel Journal of Mathematics, vol. 140, pp. 271–283, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. Habala, P. Hájek, and V. Zizler, An Introduction to Banach Space Theory, vol. 1, MatFiz Press, University of Karlovy, Prague, Czech Republic, 1996.
  11. R. R. Phelps, Convex Functions, Monotone Operators and Differentiability, vol. 1364 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1989. View at MathSciNet