A generalization of lin divergence and the derivation of a new information divergence

The f‐divergence is a general class of divergences which includes various divergences used in representing the difference between two probability densities. It was introduced by Csiszár. Lin, on the other hand, in 1991 introduced a divergence based on a new idea. the inequalities relating the divergence to the existing two divergences are shown, and the results are applied to the problems in information theory. This paper discusses the relation between the inequality concerning Lin's divergence and the inequality concerning the f‐divergence. Based on Lin's method of constructing the divergence, a new divergence called Hermite‐Hadamard divergence is introduced. the property of the proposed divergence, as well as its relation to Lin's inequality, are discussed. Using the proposed divergence, an inequality which is improved further compared to the inequality relating the Kullback diver gence and Hellinger distance is derived. Those results are derived in this paper.