Journal of Inequalities and Applications
Volume 5 (2000), Issue 1, Pages 53-61

Steffensen pairs and associated inequalities

Hillel Gauchman

Department of Mathematics, Eastern Illinois University, Charleston 61920, IL, USA

Received 22 February 1999; Revised 12 April 1999

Copyright © 2000 Hillel Gauchman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let x1,,xn be positive numbers and α2. It is known that if i=1nxiA, i=1nxiαBα, then for any k such that k(A/B)1/(α1), there are k numbers among x1,,xn whose sum is bigger than or equal to B. We express this statement saying that a pair of functions (xα,x1/(α1)) is a Steffensen pair. In this paper we show how to find many Steffensen pairs.