Let ƒ:X × Y → Z be a separately continuous mapping, where X is a Baire p-space and Z a completely regular space, and let y be a a q-point of Y. We show that: (i) ƒ is strongly quasicontinuous at each point of X × {y}, (ii) if Z is a p-space, then ƒ is subcontinuous at each point of A × {y}, where A is a dense subset of X. Then, we use (i) and (ii) to prove that every separately continuous action of a left topological group, which is a Baire p-space, in a p-space, is a continuous action. In particular, every semitopological group, which is a Baire p-space, has a continuous multiplication.