Abstract. The extremal problem $$\min_{-1\le x_1<\cdots< x_n\le1}\max_{1\le i\le n-1} \Sigma_{k=1}^i(x_{i+1}-x_k)^{-p}$$ is investigated. Its exact lower bounds are provided and the equioscillation characterizations of Bernstein and Erdős of its solution are given.

AMS Subject Classification (1991): 41A05

Received August 30, 1996. (Registered under 6105/2009.)