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On cyclic α(·)-monotone multifunctions

100%

Rolewicz S.

Studia Mathematica

2000

tom 141

nr 3

263-272

Let (X,d) be a metric space. Let Φ be a linear family of real-valued functions defined on X. Let $Γ: X → 2^{Φ}$ be a maximal cyclic α(·)-monotone multifunction with non-empty values. We give a sufficient condition on α(·) and Φ for the following generalization of the Rockafellar theorem to hold. There is a function f on X, weakly Φ-convex with modulus α(·), such that Γ is the weak Φ-subdifferential of f with modulus α(·), $Γ(x)=∂^{-α}_{Φ}f|_{x}$.

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

80%

Rolewicz S.

Studia Mathematica

1999

tom 133

nr 1

29-37

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.

Ograniczanie wyników

2 Studia Mathematica

2 Rolewicz S.

1 2000

1 1999

Wyniki wyszukiwania

On cyclic α(·)-monotone multifunctions

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