$ M$-strongly convex subsets and their generating sets
Maxim Viktorovich Balashov, Евгений Сергеевич Половинкин · Sbornik Mathematics · 2000
For subsets of a Banach space the notions of a generating set and an -strongly convex set are introduced. The latter can be represented as the intersection of sets of the form , which are translates of the generating set . A generating set must satisfy a condition that ensures a special support principle, as shown in the paper. Using this support principle a new area of convex analysis is constructed enabling one to strengthen classical results of the type of the Caratheodory and Krein-Milman theorems. Various classes of generating sets are described and the properties of -strongly convex sets are studied.