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Transactions of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

  • 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

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