On surjectivity results for maximal monotone operators of type (D)

M. Rocco; J. E. Martínez-Legaz

On surjectivity results for maximal monotone operators of type (D)

M. Rocco, J. E. Martínez-Legaz

Department of Economics and Economic History

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

A generalization of Rockafellar's surjectivity theorem was provided in [14], replacing the duality mapping by any maximal monotone operator having finite-valued Fitzpatrick function. The present paper extends this result to the nonreflexive setting for maximal monotone operators of type (D) and refines the; finite-valuedness condition on the Fitzpatrick function. Moreover, a characterization of surjectivity properties for the sum of two maximal monotone operators of type (D) in terms of Fenchel duality is given. © Heldermann Verlag.

Original language	English
Pages (from-to)	545-576
Journal	Journal of Convex Analysis
Volume	18
Issue number	2
Publication status	Published - 5 May 2011

Keywords

Bidual
Convex representation
Fenchel duality
Monotone operator
Surjectivity
Type (d)

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abstract = "A generalization of Rockafellar's surjectivity theorem was provided in [14], replacing the duality mapping by any maximal monotone operator having finite-valued Fitzpatrick function. The present paper extends this result to the nonreflexive setting for maximal monotone operators of type (D) and refines the; finite-valuedness condition on the Fitzpatrick function. Moreover, a characterization of surjectivity properties for the sum of two maximal monotone operators of type (D) in terms of Fenchel duality is given. {\textcopyright} Heldermann Verlag.",

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T1 - On surjectivity results for maximal monotone operators of type (D)

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AU - Martínez-Legaz, J. E.

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N2 - A generalization of Rockafellar's surjectivity theorem was provided in [14], replacing the duality mapping by any maximal monotone operator having finite-valued Fitzpatrick function. The present paper extends this result to the nonreflexive setting for maximal monotone operators of type (D) and refines the; finite-valuedness condition on the Fitzpatrick function. Moreover, a characterization of surjectivity properties for the sum of two maximal monotone operators of type (D) in terms of Fenchel duality is given. © Heldermann Verlag.

AB - A generalization of Rockafellar's surjectivity theorem was provided in [14], replacing the duality mapping by any maximal monotone operator having finite-valued Fitzpatrick function. The present paper extends this result to the nonreflexive setting for maximal monotone operators of type (D) and refines the; finite-valuedness condition on the Fitzpatrick function. Moreover, a characterization of surjectivity properties for the sum of two maximal monotone operators of type (D) in terms of Fenchel duality is given. © Heldermann Verlag.

KW - Bidual

KW - Convex representation

KW - Fenchel duality

KW - Monotone operator

KW - Surjectivity

KW - Type (d)

M3 - Article

VL - 18

SP - 545

EP - 576

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

SN - 0944-6532

IS - 2

ER -