Viscosity coderivatives and their limiting behavior in smooth Banach spaces

This paper concerns with generalized differentiation of set-valued and nons mooth mappings between Banach spaces. We study the so-called viscosity code rivatives of multifunctions and their limiting behavior under certain geome tric assumptions on spaces in question related to the existence of smooth b ump functions of any kind. The main results include various calculus rules for viscosity coderivatives and their topological limits. They are importan t in applications to variational analysis and optimization.