Abstract

Following some older ideas of ours and some more recent ones due to Yao, we give a self contained (except some well known results) and relatively short proof of the Rockafellar's sum theorem for the largest possible class of maximally monotone operators on a non reflexive Banach space.

Author information

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

Andrei Verona

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

averona10@yahoo.com

Maria E. Verona

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

verona@usc.edu

Keywords

  • C0-maximally monotone operator
  • convex function
  • convex set
  • Fitzpatrick function
  • maximally monotone operator
  • monotone operator
  • operator of type (FPV)
  • sum theorem

Mathematics Subject Classification

47H05; 49N15, 52A41, 90C25

Suggested citation

A. Verona, M. E. Verona. “On Rockafellar's Sum Theorem in General Banach Spaces.” Journal of Convex Analysis 29 (2022), No. 2, 381–390. https://doi.org/10.68381/jca29024

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press.