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Journal of Convex Analysis 16 (2009), No. 3, 973--986
Copyright Heldermann Verlag 2009

Positive Sets, Conservative Sets and Dissipative Sets

Jean-Paul Penot
Lab. of Applied Mathematics, Faculty of Sciences, University of Pau, BP 1155, 64013 Pau, France

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.

Keywords: Balanced space, conservative set, dissipative set, Fitzpatrick function, monotone operator, positive set, Simons space.

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

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