On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions
Volume 133 / 1999
Studia Mathematica 133 (1999), 29-37
DOI: 10.4064/sm-133-1-29-37
Abstract
Let (X,d) be a metric space. Let Φ be a family of real-valued functions defined on X. Sufficient conditions are given for an α(·)-monotone multifunction $Γ: X → 2^Φ$ to be single-valued and continuous on a weakly angle-small set. As an application it is shown that a γ-paraconvex function defined on an open convex subset of a Banach space having separable dual is Fréchet differentiable on a residual set.
