A New Characterization Of Augustin Information And Mean

A new method to characterize Augustin information and mean is proposed. The proposed method allows for briefer and more direct proofs for the previously known results and leads to new observations related to this new characterization for classical channels. For classical-quantum channels, the proposed method extends the results, such as the existence of Augustin mean and Augustin fixed point property, to models with separable Hilbert spaces at the output.