Abstract

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.

Author information

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

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

Keywords

  • Star-shaped set
  • convex relation
  • convex process
  • rate of growth
  • generalized spectral radius

Mathematics Subject Classification

52A20; 47D20, 58C06, 90C25

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Suggested citation

A. Vladimirov, A. Rubinov. “Dynamics of Positive Multiconvex Relations.” Journal of Convex Analysis 8 (2001), No. 2, 387–399. https://doi.org/10.68381/jca08019

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Published by Heldermann Verlag, 2001. Rights now held by Banach Press LLC.