Analysis of a class of non linear subdivision schemes and associated   multi-resolution transforms
  This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a contractivity property, stability and convergence are derived. These results are then applied to various schemes such as uncentered interpolatory linear scheme, WENO scheme [13], Power-P scheme [16] and a non linear scheme using local spherical coordinates [18]. 
S. Amat, K. Dadourian, J. Liandrat