Journal of Inequalities and Applications (Jan 2010)
Multiplicative Concavity of the Integral of Multiplicatively Concave Functions
Abstract
We prove that G(x,y)=|∫yxf(t)dt| is multiplicatively concave on [a,b]×[a,b] if f:[a,b]⊂(0,∞)→(0,∞) is continuous and multiplicatively concave.