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A converse to the Lions-Stampacchia theorem

Emil Ernst, Michel Théra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.

A converse to the Lions-Stampacchia Theorem

Emil Ernst, Michel Théra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.

A geometric approach to accretivity

Leonid V. Kovalev (2007)

Studia Mathematica

We establish a connection between generalized accretive operators introduced by F. E. Browder and the theory of quasisymmetric mappings in Banach spaces pioneered by J. Väisälä. The interplay of the two fields allows for geometric proofs of continuity, differentiability, and surjectivity of generalized accretive operators.

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