Hammadi, Nesrine2021-07-152021-07-152021http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/25042In the first chapter, we introduce preliminary notions about Lipschitz space, and the properties of Lipschitz functions. Then in the second chapter we present some fundamental results related to the Lipschitzian operators on the free lipschitz space F (M) . Finally in the last chapter we give some results about the non-linear isometries, and the isometric universal shifting property (infinite shift space).enFree Lipschitz spaces, Metric separable space, convex sub-space, isometry, affine mapping, universal characteristic of the shifting propertyThesis