Journal of Inequalities and Applications 
Volume 5 (2000), Issue 1, Pages 53-61
doi:10.1155/S1025583400000047

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

Abstract

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.