MEKDOUR, Fateh2018-07-012018-07-012018https://repository.univ-msila.dz/handle/123456789/5047We will study the generalization of the Daugavet property of the linear case to the nonlinear case; more precisely the Lipschitz case. Among other, we are interested in a some conditions sufficient for a Lipschitz operator to satisfy the Daugavet's property.enDaugavet property, Lipschitz operator, 1  -singular operator, strong Radon-Nikodým operator, copies spaces of 1  , the slice of the unit ball X B , the Lipschitz slice of , X S slope (T) set and SCD set.Thesis