Kodai Mathematical Seminar Reports

A characterization of convex subsets of normed spaces

Hilton Vieira Machado

Full-text: Open access

Article information

Source
Kodai Math. Sem. Rep., Volume 25, Number 3 (1973), 307-320.

Dates
First available in Project Euclid: 1 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138846819

Digital Object Identifier
doi:10.2996/kmj/1138846819

Mathematical Reviews number (MathSciNet)
MR0326359

Zentralblatt MATH identifier
0271.54021

Subjects
Primary: 46B99: None of the above, but in this section

Citation

Machado, Hilton Vieira. A characterization of convex subsets of normed spaces. Kodai Math. Sem. Rep. 25 (1973), no. 3, 307--320. doi:10.2996/kmj/1138846819. https://projecteuclid.org/euclid.kmj/1138846819


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References

  • [1] BLUMENTHAL, L. M., Theory and applications of distance geometry. Oxford (1953).
  • [2] BLUMENTHAL, L. M., AND K. MENGER, Studies in geometry. San Francisco (1970)
  • [3] BROWDER, F. E., Nonexpansive nonlinear operators in Banach spaces. Proc. Nat Acad. Sci.U. S. A. 54 (1965), 1041-1044.
  • [4] DUNFORD, N., AND J. T. SCHWARTZ, Linear operators. New York (1955)
  • [5] KIJIMA, Y. AND W. TAKAHASHI, A fixed-point theorem for nonexpansive map pings in metric space. Kdai Math. Sem. Rep.21 (1969), 326-330.
  • [6] KIRK, W. A., A fixed-point theorem for mappings which do not increase dis tance. Amer. Math. Monthly 72 (1965), 1004-1006.
  • [7] MACHADO, H. V., Fixed-point theorems for nonexpansive mappings in metri spaces with normal structure. Ph. D. thesis, Chicago (1971).
  • [8] TAKAHASHI, W., A convexity in metric space and nonexpansive mappings, I. Kdai Math. Rep.22 (1970), 142-149