  In this paper, we consider the stochastic averaging principle and stability
for multi-valued McKean-Vlasov stochastic differential equations with jumps.
First, under certain averaging conditions, we are able to show that the
solutions of the equations concerned can be approximated by solutions of the
associated averaged multi-valued McKean-Vlasov stochastic differential
equations with jumps in the sense of the mean square convergence. Second, we
extend the classical It\^{o}'s formula from stochastic differential equations
to multi-valued McKean-Vlasov stochastic differential equations with jumps.
Last, as application of It\^{o}'s formula, we present the exponential stability
of second moments, the exponentially 2-ultimate boundedness and the almost
surely asymptotic stability for their solutions in terms of a Lyapunov
function.
