Journal of Inequalities and Applications
Volume 3 (1999), Issue 4, Pages 331-347
doi:10.1155/S1025583499000235
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.