An Inequality for Bounded Functions

In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)Comment: 7 page

Bounds for the Ratios of Differences of Power Means in Two Arguments

Using methods from classical analysis, sharp bounds for the ratio of differences of Power Means are obtained. Our results generalize and extend previous ones due to S. Wu(2005), and to S. Wu and L. Debnath.Comment: 1 figur