Journal of Inequalities and Applications
Volume 3 (1999), Issue 4, Pages 331-347
doi:10.1155/S1025583499000235
On a modified version of Jensen inequality
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.
Abstract
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∈ℝ, 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.