Representations for Maximal Monotone Operators of Type (D) in Banach Spaces

Bao T. Nguyen (), Tran N. Nguyen () and Huynh M. Hien ()
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Bao T. Nguyen: Quy Nhon University
Tran N. Nguyen: Quy Nhon University
Huynh M. Hien: Quy Nhon University

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 1, 19 pages

Abstract: Abstract The present paper 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.

Keywords: Maximal monotone operator; Monotone operator of type (D); Minimal-norm selection; w-Kadec-Klee-property; w $$^*$$ ∗ -Kadec-Klee-property; Strictly convex space; 47H05; 47H04; 47N10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02457-8

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