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Journal of Convex Analysis 10 (2003), No. 1, 149--168
Copyright Heldermann Verlag 2003

On Pseudomonotone Maps T for which -T is also Pseudomonotone

Monica Bianchi
Istituto di Econometria e Matematica per le Decisioni Economiche, Universita Cattolica, Via Necchi 9, 20123 Milano, Italy,

Nicolas Hadjisavvas
Dept. of Product and Systems Design, University of the Aegean, 84100 Hermoupolis, Syros, Greece,

Siegfried Schaible
A. G. Anderson Graduate School of Management, University of California, Riverside, CA 92521-0203, U.S.A.,

Recently pseudomonotone variational inequalities have been studied quite extensively, hereby extending the theory of pseudoconvex minimization problems. The focus of the present work are "pseudoaffine maps", i.e., pseudomonotone maps T for which -T is also pseudomonotone. A particular case of such maps are the gradients of pseudolinear functions. Our main goal is to derive the general form of pseudoaffine maps which are defined on the whole space.

Keywords: Pseudoconvex function, pseudolinear function, pseudomonotone map, pseudoaffine map.

MSC 2000: 26B25, 47N10, 47H99.

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