Mean-reflected G-BSDEs with multi-variate constraints

In this paper, we consider the multi-dimensional reflected backward stochastic differential equation driven by [Formula: see text]-Brownian motion ([Formula: see text]-BSDE) with a multi-variate constraint on the [Formula: see text]-expectation of its solution. The generators are diagonally dependent on [Formula: see text] and on all [Formula: see text]-components. We establish the existence and uniqueness results through a fixed-point argument.