ArticleOriginal scientific text
Title
On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions
Authors 1
Affiliations
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland
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 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.
Keywords
Fréchet Φ-differentiability, γ-paraconvex functions, α(·)-monotone multifunctions
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