Skip to main content
Log in

Weak convergence of convex sets in Banach spaces

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. M.Baronti and P. L.Papini, Convergence of sequences of sets. Functional analysis and approximation theory (Proc. Internat. Conf., Bombay, 1985), International Series of Numerical Analysis76, Basel 1986.

  2. G.Beer and V.Klee, Limits of starshaped sets. To appear.

  3. W.Blaschke, Kreis and Kugel. Leipzig 1916.

  4. G. Choquet, Convergences. Ann. Univ. Grenoble, Sect. Sci. Mat. Phys. (N.S)23, 7–112 (1948).

    Google Scholar 

  5. N.Dunford and J. T.Schwartz, Linear Operators, Part I. New York 1958.

  6. S. Francaviglia, A. Lechiki andS. Levi, Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions. J. Math. Anal. Appl.112, 347–370 (1985).

    Google Scholar 

  7. L. Hörmander, Sur la fonction d'appui des ensembles convexes dans un espace localement convex. Ark. Mat.3, 181–186 (1955).

    Google Scholar 

  8. K.Kuratowski, Topology. New York 1966.

  9. U. Mosco, Convergence of convex sets and of solutions of variational inequalities. Adv. in Math.3, 510–585 (1969).

    Google Scholar 

  10. G. Salinetti andR. J. B. Wets, On the convergence of sequences of convex sets in finite dimension. SIAM Review21, 18–33 (1979).

    Google Scholar 

  11. F. A.Valentine, Convex sets. New York 1964.

  12. R. A. Wijsman, Convergence of sequences of convex sets, cones and functions II. Trans. Amer. Math. Soc.123, 32–45 (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Blasi, F.S., Myjak, J. Weak convergence of convex sets in Banach spaces. Arch. Math 47, 448–456 (1986). https://doi.org/10.1007/BF01189987

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01189987

Keywords

Navigation