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Journal of Convex Analysis 08 (2001), No. 2, 387--400
Copyright Heldermann Verlag 2001

Dynamics of Positive Multiconvex Relations

A. Vladimirov
Institute for Information Transmission Problems, Russian Academy of Sciences, 19 Bol'shoi Karetnyi st., 101447 Moscow, Russia

A. Rubinov
School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria 3353, Australia

A notion of multiconvex relation as a union of a finite number of convex relations is introduced. For a particular case of multiconvex process, that is, a union of a finite set of convex processes, we define the notions of the joint and the generalized spectral radius in the same manner as for matrices. We prove the equivalence of these two values if all component processes are positive, bounded, and closed.

Keywords: Star-shaped set, convex relation, convex process, rate of growth, generalized spectral radius.

MSC: 52A20; 47D20, 58C06, 90C25.

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