  We obtain asymptotic mean-value formulas for solutions of second-order
elliptic equations. Our approach is very flexible and allows us to consider
several families of operators obtained as an infimum, a supremum, or a
combination of both infimum and supremum, of linear operators. The families of
equations that we consider include well-known operators such as Pucci, Issacs,
and $k$-Hessian operators.
