Journal of Inequalities and Applications
Volume 3 (1999), Issue 4, Pages 331-347

On a modified version of Jensen inequality

Tomasz Szostok

Institute of Mathematics, Silesian University, Bankowa 14, Katowice 40-007, Poland

Received 11 May 1998; Revised 12 August 1998

Copyright © 1999 Tomasz Szostok. 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.


The right-hand side of the Jensen inequality is multiplied by a constant and the related equation is considered. It is shown that every continuous solution of this equation is of the form f(x)=cxd for some c, d(,0)(1,). Further, it is proved that some functions satisfying the inequality considered are bounded below but not above by suitable solutions of the corresponding equation.