Abstract

We look for a simple general framework which would encompass the notion of symmetric self-dual spaces introduced by S. Simons and the notion of self-paired product space proposed recently by the author ["Monotonicities and dualities", in: Generalized Convexity and Related Topics, I. V. Konnor, D. T. Luc and A. M. Rubinov (eds), Lecture Notes in Economics and Math. Systems 583, Springer, Berlin (2007), 300-414]. Such a framework is appropriate for the study of a notion generalizing the concept of monotone operator. The representation of such operators by functions is the main purpose of the study.

Author information

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

Jean-Paul Penot

Lab. of Applied Mathematics, Faculty of Sciences, University of Pau, BP 1155, 64013 Pau, France
and: UMR CNRS 5142, Pau, France

jean-paul.penot@univ-pau.fr

Keywords

  • Balanced space
  • conservative set
  • dissipative set
  • Fitzpatrick function
  • monotone operator
  • positive set
  • Simons space

Mathematics Subject Classification

47H05, 47H06, 47B44, 47A07, 11E05

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Suggested citation

J.-P. Penot. “Positive Sets, Conservative Sets and Dissipative Sets.” Journal of Convex Analysis 16 (2009), No. 3&4, 973–986. https://doi.org/10.68381/jca16059

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press LLC.