Borwein, J. M.; Strojwas, H. M. Proximal analysis and boundaries of closed sets in Banach space. I: Theory. (English) Zbl 0577.46011 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. Cited in 4 ReviewsCited in 40 Documents MSC: 46B20 Geometry and structure of normed linear spaces 46A55 Convex sets in topological linear spaces; Choquet theory Keywords:proximal normal formulas PDF BibTeX XML Cite \textit{J. M. Borwein} and \textit{H. M. Strojwas}, Can. J. Math. 38, 431--452 (1986; Zbl 0577.46011) Full Text: DOI