What type of convergent boundary is mount Vesuvius?
A rather complicated convergence situation.
This is a bit of a complicated situation - see pic. Apologies that it is so small. Vesuvius is part of the Campanian volcanic arc, a line of volcanoes that formed over a subduction zone created by the convergence of the African and Eurasian plates.
This subduction zone stretches the length of the Italian peninsula, and is also the source of other volcanoes like Mount Etna, the Phlegraean Fields (Campi Flegrei), Vulcano, and Stromboli. Under Vesuvius, the lower part of the subducting slab has torn and detached from the upper part to form what is called a "slab window". This makes Vesuvius' rocks slightly different chemically from the rocks erupted from the other Campanian volcanoes.