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Displaying similar documents to “Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces”

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).

Inertial forward-backward splitting method in Banach spaces with application to compressed sensing

Prasit Cholamjiak, Yekini Shehu (2019)

Applications of Mathematics

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We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces. ...

Weak uniform normal structure in direct sum spaces

Tomás Domínguez Benavides (1992)

Studia Mathematica

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The weak normal structure coefficient WCS(X) is computed or bounded when X is a finite or infinite direct sum of reflexive Banach spaces with a monotone norm.

An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators

A. Renaud, G. Cohen (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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To find a zero of a maximal monotone operator, an extension of the Auxiliary Problem Principle to nonsymmetric auxiliary operators is proposed. The main convergence result supposes a relationship between the main operator and the nonsymmetric component of the auxiliary operator. When applied to the particular case of convex-concave functions, this result implies the convergence of the parallel version of the Arrow-Hurwicz algorithm under the assumptions of Lipschitz and partial...

Plurisubharmonic functions on compact sets

Rafał Czyż, Lisa Hed, Håkan Persson (2012)

Annales Polonici Mathematici

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Poletsky has introduced a notion of plurisubharmonicity for functions defined on compact sets in ℂⁿ. We show that these functions can be completely characterized in terms of monotone convergence of plurisubharmonic functions defined on neighborhoods of the compact.