  The effect of quantum steering describes a possible action at a distance via
local measurements. Whereas many attempts on characterizing steerability have
been pursued, answering the question as to whether a given state is steerable
or not remains a difficult task. Here, we investigate the applicability of a
recently proposed method for building steering criteria from generalized
entropic uncertainty relations. This method works for any entropy which satisfy
the properties of (i) (pseudo-) additivity for independent distributions; (ii)
state independent entropic uncertainty relation (EUR); and (iii) joint
convexity of a corresponding relative entropy. Our study extends the former
analysis to Tsallis and R\'enyi entropies on bipartite and tripartite systems.
As examples, we investigate the steerability of the three-qubit GHZ and W
states.
