Pairs of monotone operators

Author:
S. Simons

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

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

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

MathSciNet review:
1458312

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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 and Isaac Namioka,*Linear topological spaces*, With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. MR**0166578****3.**Robert R. Phelps,*Convex functions, monotone operators and differentiability*, 2nd ed., Lecture Notes in Mathematics, vol. 1364, Springer-Verlag, Berlin, 1993. MR**1238715****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