Lipschitz slices and the Daugavet equation for Lipschitz operators
  We introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer to the non-linear case some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators. 
Vladimir Kadets, Miguel Martin, Javier Meri, and Dirk Werner
math.FA