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

被引：0
|
作者：
Nguyen, Bao T. [1 ]
Nguyen, Tran N. [1 ]
Hien, Huynh M. [1 ]
机构：
[1] Quy Nhon Univ, Dept Math & Stat, 170 Duong Vuong, Quy Nhon, Vietnam
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2024年
关键词：
Maximal monotone operator; Monotone operator of type (D); Minimal-norm selection; w-Kadec-Klee-property; w*-Kadec-Klee-property; Strictly convex space;
D O I：
10.1007/s10957-024-02457-8
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
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.
引用
收藏
页数：19
相关论文
共 50 条
  • [1] On the convergence of sequence of maximal monotone operators of type (D) in Banach spaces
    Pattanaik, S. R.
    Pradhan, D. K.
    [J]. POSITIVITY, 2019, 23 (04) : 1009 - 1020
  • [2] On the convergence of sequence of maximal monotone operators of type (D) in Banach spaces
    S. R. Pattanaik
    D. K. Pradhan
    [J]. Positivity, 2019, 23 : 1009 - 1020
  • [3] ε-Enlargements of maximal monotone operators in Banach spaces
    Burachik, RS
    Svaiter, BF
    [J]. SET-VALUED ANALYSIS, 1999, 7 (02): : 117 - 132
  • [4] ε-Enlargements of Maximal Monotone Operators in Banach Spaces
    Regina Sandra Burachik
    B. F. Svaiter
    [J]. Set-Valued Analysis, 1999, 7 : 117 - 132
  • [5] Sum of Ultra Maximal Monotone Operators and Operators of Type (D) in Grothendieck Spaces
    Pradhan, D. K.
    Pattanaik, S. R.
    [J]. THAI JOURNAL OF MATHEMATICS, 2018, 16 : 63 - 75
  • [6] Monotone type operators in nonreflexive Banach spaces
    Yuqing Chen
    Yeol Je Cho
    [J]. Fixed Point Theory and Applications, 2014
  • [7] Monotone type operators in nonreflexive Banach spaces
    Chen, Yuqing
    Cho, Yeol Je
    [J]. FIXED POINT THEORY AND APPLICATIONS, 2014,
  • [8] Strong convergence theorems for maximal monotone operators in Banach spaces
    Ceng, L. C.
    Schaible, S.
    Yao, J. C.
    [J]. OPTIMIZATION, 2010, 59 (06) : 807 - 819
  • [9] Calculus rules for maximal monotone operators in general Banach spaces
    Voisei, M. D.
    [J]. JOURNAL OF CONVEX ANALYSIS, 2008, 15 (01) : 73 - 85
  • [10] Lower Limits of Type (D) Monotone Operators in General Banach Spaces
    Bueno, Orestes
    Garcia, Yboon
    Alves, Maicon Marques
    [J]. JOURNAL OF CONVEX ANALYSIS, 2016, 23 (02) : 333 - 345
12345