ACTA issues

A kind of extremal problems of integrations on an arbitrary measure

Ying Guang Shi

Acta Sci. Math. (Szeged) 65:3-4(1999), 567-575
2703/2009

 Abstract. Let $d\alpha$ be a measure on $[a,b]$ and let $p_k\ge1$, $k=1,2,\ldots,n$, be arbitrary fixed real numbers. The existence, uniqueness, and characterizations of a solution of the extremal problem $$\min_{a< x_1\le\ldots \le x_n\le b}\int_a^b\prod_{k=1}^n|x-x_k|^{p_k}d\alpha(x)$$ are given. AMS Subject Classification (1991): 41A55, 65D32 Received May 21, 1998, and in revised form February 25, 1999. (Registered under 2703/2009.)