The principle of optimality of dynamic programming is used to prove three major inequalities due to Shannon, Renyi and Holder. The inequalities are then used to obtain some useful results in information theory. In particular measures are obtained to measure the mutual divergence among two or more probability distributions.

Divergence measures, dynamic programming, Renyi and Holder inequalities, Shannon
dx.doi.org/10.1155/S016117128700070X
International Journal of Mathematics and Mathematical Sciences
Sprott School of Business

Kapur, J.N. (J. N.), Kumar, V, & Kumar, U. (1987). A Measure of Mutual Divergence Among a Number of Probability Distributions. International Journal of Mathematics and Mathematical Sciences, 10(3), 597–607. doi:10.1155/S016117128700070X