We define N-Chebyshev sets in a Banach space X for every positive integer N (when N = 1, these are ordinary Chebyshev sets) and study conditions that guarantee their convexity. In particular, we prove that all N-Chebyshev sets are convex when N is even and X is uniformly convex or N ≥ 3 is odd and X is smooth uniformly convex.
展开▼
