  We give necessary and sufficient conditions for the existence of a
generalization of R\'enyi divergence, which is defined in terms of a deformed
exponential function. If the underlying measure $\mu$ is non-atomic, we found
that not all deformed exponential functions can be used in the generalization
of R\'enyi divergence; a condition involving the deformed exponential function
is provided. In the case $\mu$ is purely atomic (the counting measure on the
set of natural numbers), we show that any deformed exponential function can be
used in the generalization.
