Abstract
For a Banach space X, a new constant G(X)=sup {λ(X) | A ⊂ X, d(A)=1} is introduced. The main result is that G (X) coincides with the Jung constant J (X) (Theorem 1), which yields an estimate for the latter. Some other results concerning J (X) and the measure of nonconvexity λ are given. Bibliography: 5 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature Cited
D. Amir, “On Jung's constant and related constants in normed linear spaces,”Pacific J. Math.,118, 1–15 (1985).
J. Eisenfeld and V. Lakshmikantham, “On a measure of nonconvexity and applications,”Yokohama Math. J.,24, 133–140 (1976).
V. Klee, “Circumspheres and inner product,”Math. Scand.,8, 363–370 (1960).
J. Lindenstrauss and H. P. Rosenthal, “TheL p -spaces,”Israel J. Math.,7, 325–349 (1969).
E. Maluta, “Uniformly normal structure and related coefficients,”Pacific J. Math.,111, 357–369 (1984).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 208, 1993, pp. 174–181.
Translated by O. A. Ivanov.
Rights and permissions
About this article
Cite this article
Gulevich, N.M. The measure of nonconvexity and the jung constant. J Math Sci 81, 2562–2566 (1996). https://doi.org/10.1007/BF02362426
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02362426