Journal of Convex Analysis 15 (2008), No. 1, 001--015
Copyright Heldermann Verlag 2008
Differentiability of Approximately Convex, Semiconcave and Strongly Paraconvex Functions
Ludek Zajícek
Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic
zajicek@karlin.mff.cuni.cz
It is shown that continuous approximately convex, semiconcave and strongly α( . )-paraconvex functions on Banach spaces have almost all (but not all) known first order differentiability properties of continuous convex functions. The main results easily follow from known (or essentially known) results on single-valuedness and continuity of submonotone operators.
Keywords: Approximately convex function, semiconcave function, strongly alpha-cdot-paraconvex function, submonotone operator, Frechet differentiability, Gateaux differentiability.
MSC: 46G05; 49J50
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