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Local analysis of a cubically convergent method for variational inclusions

Steeve Burnet, Alain Pietrus (2011)

Applicationes Mathematicae

This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from q to the closed subsets of q . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.

Local Lipschitz continuity of the stop operator

Wolfgang Desch (1998)

Applications of Mathematics

On a closed convex set Z in N with sufficiently smooth ( 𝒲 2 , ) boundary, the stop operator is locally Lipschitz continuous from 𝐖 1 , 1 ( [ 0 , T ] , N ) × Z into 𝐖 1 , 1 ( [ 0 , T ] , N ) . The smoothness of the boundary is essential: A counterexample shows that 𝒞 1 -smoothness is not sufficient.

Locally admissible multi-valued maps

Mirosław Ślosarski (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.

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