Lower Limits of Type (D) Monotone Operators in general Banach Spaces

2014/12/19 by Orestes Bueno, Bueno, Orestes, Yboon García +3
Computer Science · Mathematics · #46H05 #46N10 #49J52 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1412.6195

openalex publication_date 2014/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give, for general Banach spaces, a characterization of the sequential lower limit of maximal monotone operators of type (D) and prove its representability. As a consequence, using a recent extension of the Moreau-Yosida regularization for type (D) operators, we extend to general Banach spaces the definitions of the variational sum of monotone operators and the variational composition of monotone operators with continuous linear mappings, and we prove that both operators are representable.

Related

• Limits of sequences of maximal monotone operators
• Limits of maximal monotone operators driven by their representative functions
• Recent progress on Monotone Operator Theory
• Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex
• Sum of two maximal monotone operators in a general Banach space is maximal