Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex

Nguyen B. Tran; Tran N. Nguyen; Huynh M. Hien

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arXiv · 2401.00293

Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex

Nguyen B. Tran·Tran N. Nguyen·Huynh M. Hien

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Abstract

This work deals with a maximal monotone operator $A$ of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value $Ax$ at a given point $x$ via its values at nearby points of $x$. We show that the faces of $Ax$ are contained in the set of all weak$^*$ convergent limits of bounded nets of the operator at nearby points of $x$, then we obtain a representation for $Ax$ by use of this set. In addition, representations for the support function of $Ax$ based on the minimal-norm selection of the operator in certain Banach spaces are given.

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BibTeX RIS

Nguyen B. Tran, Tran N. Nguyen, Huynh M. Hien. 2023-12-30. Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex. https://arxiv.org/abs/2401.00293

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