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