Title: On The Equivalence of Projections In Relative $α$-Entropy and Rényi Divergence,
Abstract: The aim of this work is to establish that two recently published projection
theorems, one dealing with a parametric generalization of relative entropy and
another dealing with Rényi divergence, are equivalent under a
correspondence on the space of probability measures. Further, we demonstrate
that the associated "Pythagorean" theorems are equivalent under this
correspondence. Finally, we apply Eguchi's method of obtaining Riemannian
metrics from general divergence functions to show that the geometry arising
from the above divergences are equivalent under the aforementioned
correspondence.