Favorable Classes of Mappings and Multimappings in Nonlinear Analysis and Optimization

A generalization of the class of lower $C^k$−functions introduced by R.T. Rockafellar [28] called lower $T^k$−functions is proposed in the infinite dimensional case. Mappings of class $T^k$ are studied for themselves as they seem to deserve some attention. Other classes of functions such as subconvex functions, subsmooth functions, semismooth functions are either introduced or extended to the case of an infinite dimensional Banach space.