Rényi entropy, Rényi divergence, Jensen-Rényi information generating functions and properties

In this paper, we propose R\'enyi information generating function (RIGF) and discuss its various properties. The relation between the RIGF and Shannon entropy of order q > 0 is established. Several bounds are obtained. The RIGF of escort distribution is derived. Furthermore, we introduce R\'enyi divergence information generating function (RDIGF) and show its effect under monotone transformations. Finally, we propose Jensen-R\'enyi information generating function (JRIGF) and introduce its several properties.