Proximal analysis and boundaries of closed sets in Banach space. I: Theory. (English) Zbl 0577.46011

Borwein, J. M.; Strojwas, H. M.

Can. J. Math. 38, 431-452 (1986).

In this part I we extend ”lim inf” formulas and proximal normal formulas and lift other proximal analytical theorems from finite dimensional spaces to reflexive Banach spaces. In Part II we give many applications in nonsmooth analysis, geometry of normed spaces and differentiability theory.

MSC:

46B20	Geometry and structure of normed linear spaces
46A55	Convex sets in topological linear spaces; Choquet theory

Keywords:

proximal normal formulas