On generic second-order Gateaux differentiability

Title: On generic second-order Gateaux differentiability
Creator: Borwein, J. M.; Fabian, M.
Relation: Nonlinear Analysis, Theory, Methods & Applications Vol. 20, Issue 12, p. 1373-1382
Publisher Link: http://dx.doi.org/10.1016/0362-546X(93)90166-P
Publisher: Pergamon
Resource Type: journal article
Date: 1993
Description: LET f: X → ℝ BE A function on a Banach space X. We say that f is strictly Gateaux differentiable if it is Gateaux differentiable at every point of X and the mapping (x, h) ↦ ’(x), h) is continuous. Recall that a convex Gateaux differentiable function is strictly Gateaux differentiable. In the case of a locally Lipschitz function our definition coincides with more standard ones: it requires that f^’ be norm to weak-star continuous.
Subject: separable space; residual space; second-order difference quotient; twice Gateaux differentiability
Identifier: http://hdl.handle.net/1959.13/940958
Identifier: uon:13141
Identifier: ISSN:0362-546X
Language: eng
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