Is it possible for a DPDA(deterministic pushdown automaton) to have both transitions: (q, aw, xyz) -> (q, w, yz) and (q, bw, xyz) -> (q1, bw, xyz)?

Question

Where aw/bw are input contents & xyz/yz are stack contents.
If captioned question is yes. Than expressed these 2 transitions by delta transition form:

delta(q, a, x) = (q, epsi)
delta(q, epsi, epsi) = (q1, epsi)

Above 2 transitions is not allowed to exist simutaneously in a deterministic pushdown automaton.
Is this a limitation of express power with delta transition form?