ArticleOriginal scientific text

Title

On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions

Authors 1

Affiliations

  1. 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 Γ:X2Φ 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

Bibliography

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Pages:
29-37
Main language of publication
English
Received
1998-01-12
Accepted
1998-06-04
Published
1999
Exact and natural sciences