Displaying similar documents to “Lectures on maximal monotone operators.”

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

Radu Ioan Boţ, Sorin-Mihai Grad (2011)

Open Mathematics

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In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation...

On maximal monotone operators with relatively compact range

Dariusz Zagrodny (2010)

Czechoslovak Mathematical Journal

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It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator T can be approximated by a sequence of maximal monotone operators of type NI, which converge to T in a reasonable sense (in the sense of Kuratowski-Painleve convergence).

Equilibrium of maximal monotone operator in a given set

Dariusz Zagrodny (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].

On the maximality of the sum of two maximal monotone operators.

Hassan Riahi (1990)

Publicacions Matemàtiques

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In this paper we deal with the maximal monotonicity of A + B when the two maximal monotone operators A and B defined in a Hilbert space X are satisfying the condition: U λ (dom B - dom A) is a closed linear subspace of X.