Auslander's Formula for contravariantly finite subcategories

A relative version of Auslander's formula with respect to a contravariantly finite subcategory will be given. Dual version will be treated. Several examples and applications will be provided. In particular, we show that under certain circumstances, if relative Auslander algebras of artin algebras $\Lambda$ and $\Lambda'$ are Morita equivalent, then $\Lambda$ and $\Lambda'$ are also Morita equivalent.