On the Convexity of the Closure of the Domain/Range of a Maximally Monotone Operator

Maria E. Verona; Andrei Verona

Abstract

We prove that a sufficient condition (due to Simons) for the convexity of the closure of the domain/range of a monotone operator is also necessary when the operator has bounded domain/range and is maximal.

Author information

Contact details are reproduced from the original publication and may be historical.

Maria E. Verona

Dept. of Mathematics, University of Southern California, Los Angeles, U.S.A.

verona@usc.edu

Andrei Verona

Dept. of Mathematics, California State University, Los Angeles, U.S.A.

averona10@yahoo.com

Keywords

Monotone operator
maximally monotone operator
Fitzpatrick function
Simons' conditions
type (FP)

Mathematics Subject Classification

47H05; 47A65

Suggested citation

M. E. Verona, A. Verona. “On the Convexity of the Closure of the Domain/Range of a Maximally Monotone Operator.” Journal of Convex Analysis 29 (2022), No. 3, 789–794.