Banach-Steinhaus type theorem in locally convex spaces for \(\sigma\)-locally Lipschitzian convex processes. (English) Zbl 1324.49013

Lahrech, S.; Jaddar, A.; Hlal, J.; Ouahab, A.; Mbarki, A.

Vladikavkaz. Mat. Zh. 10, No. 2, 32-35 (2008).

Summary: The main purpose of this paper is to generalize the Banach-Steinhaus theorem in locally convex spaces for \(\sigma\)-locally Lipschitzian operators established by S. Lahrech in [Miskolc Math. Notes 6, No. 1, 43–45 (2005; Zbl 1087.47035)] to \(\sigma\)-locally Lipschitzian convex processes.

MSC:

49J52	Nonsmooth analysis
49J50	Fréchet and Gateaux differentiability in optimization
47B37	Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46A45	Sequence spaces (including Köthe sequence spaces)

Keywords:

\(\sigma \)-locally Lipschitzian convex process; locally convex space; Banach-Steinhaus theorem