On measure of nonconvexity and Jung constant

For a Banach space $X$, a new constant $G(X)=\sup\{\lambda(A)\colon A\subset X,\ d(A)=1\}$ 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 $\lambda$ are given. Bibliography: 5 titles.