Recently, S.S. Dragomir used the concavity property of the log mapping and the weighted arithmetic mean-geometric mean inequality to develop new inequalities that were then applied to Information Theory. Here we extend these inequalities and their applications.

We give bounds on the difference between weighted arithmetic mean and geometric mean. These imply refined Young inequalities reverses of inequality. also study some properties Applying newly obtained inequalities, we show results Tsallis divergence, R\'{e}nyi Jeffreys-Tsallis divergence Jensen-Shannon-Tsallis divergence.

For a,b > 0 with a = b , let P = (a− b)/(4arctana/b−π) , A = (a+ b)/2 , G = √ ab denote the Seiffert mean, arithmetic mean, geometric mean of a and b , respectively. In this paper, we present new sharp bounds for Seiffert P in terms of weighted power means of arithmetic mean A and geometric mean G : ( 2 3 A p1 + 3 G p1 )1/p1 < P < ( 2 3 A p2 + 3 G p2 )1/p2 , where p1 = 4/5 and p2 = logπ/2 (3/2)...

The estimation of a mean of a proportion is a frequent task in statistical survey analysis, and often such ratios are estimated from compositions such as income components, wage components, tax components, etc. In practice, the weighted arithmetic mean is regularly used to estimate the center of the data. However, this estimator is not appropriate if the ratios are estimated from compositions, ...

respectively We note that these operators are quite di erent in the sense that the rst one fo cuses the total weight on only one argument pro jection on the rst argument whereas the second one distributes the total weight among all the ar guments evenly arithmetic mean In order to capture this idea one can de ne a measure of dispersion associated to the weight vector of the weighted arithmetic ...