Towards viscosity approximations of hierarchical fixed-point problems

We introduce methods which seem to be a new and promising tool in hierarchical fixed-point problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods for fixed-point problems. The limit attained by these curves is the solution of the general variational inequality, [inline-graphic not available: see fulltext], where [inline-graphic not available: see fulltext] denotes the normal cone to the set of fixed point of the original nonexpansive mapping [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext] a suitable nonexpansive mapping criterion. The link with other approximation schemes in this field is also made.