Upper Bounds on the Probability of Error in terms of Mean Divergence Measures

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of mean considered is convex functions. Applying some properties, upper bounds on the probability of error are established in this paper. It is also shown that the results obtained are sharper than obtained directly applying known inequalities.