Pairs of monotone operators

Author:
S. Simons

Journal:
Trans. Amer. Math. Soc. **350** (1998), 2973-2980

MSC (1991):
Primary 47H05; Secondary 46B10

DOI:
https://doi.org/10.1090/S0002-9947-98-02104-7

Addendum:
Tran. Amer. Math. Soc. 350 (1998), no. 7, 2973-2980.

MathSciNet review:
1458312

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Abstract | References | Similar Articles | Additional Information

Abstract: This note is an addendum to *Sum theorems for monotone operators and convex functions*. In it, we prove some new results on convex functions and monotone operators, and use them to show that several of the constraint qualifications considered in the preceding paper are, in fact, equivalent.

**1.**M. Coodey and S. Simons,*The convex function determined by a multifunction*, Bull. Austral. Math. Soc.**54**(1996), 87-97. CMP**96:16****2.**J. L. Kelley, I. Namioka et al.,*Linear Topological Spaces*, Van Nostrand, Princeton, 1963. MR**29:3851****3.**R. R. Phelps,*Convex Functions, Monotone Operators and Differentiability*, Lecture Notes in Mathematics**1364**(Second Edition), Springer-Verlag, Berlin, 1993. MR**94f:46055****4.**S. Simons,*Sum theorems for monotone operators and convex functions*, Trans. Amer. Math. Soc.,**350**(1998), 2953-2972.

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Additional Information

**S. Simons**

Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106-3080

Email:
simons@math.ucsb.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-02104-7

Keywords:
Banach space,
reflexivity,
maximal monotone operator,
sum theorem,
constraint qualification,
proper convex lower semicontinuous function

Received by editor(s):
December 10, 1996

Article copyright:
© Copyright 1998
American Mathematical Society