An implicit function theorem for one-sided Lipschitz mappings (Q645065)

Using a local existence theorem for the solution of a zero-point inclusion \[ 0\in F(x),\;x\in \mathbb{R}^m, \] the authors obtain both local and global implicit function theorems for set-valued equations with relaxed one-sided Lipschitz set-valued operators \(F:\mathbb{R}^k\times \mathbb{R}^m\to P_{cp,cv}(\mathbb{R}^m)\). Finally, as an application, Crank-Nicolson schemes for differential inclusions and differential algebraic inclusions are given.