Convex selections of multifunctions and their applications†

Authors: Michta, Mariusz¹; Motyl, Jerzy¹

Source: Optimization, Volume 55, Numbers 1-2, -02/February–April 2006 , pp. 91-99(9)

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Abstract:

The notion of upper separated set-valued functions which forms a necessary and sufficient condition for the existence of convex selections for convex-valued multifunctions is introduced. The results obtained in this article lead to a new class of the multifunctions admitting continuous selections and therefore they are applicable to the existence of solutions to differential and stochastic inclusions.

Keywords: Upper separated multifunction; Legendre–Fenchel transform; Differential and stochastic inclusion

Document Type: Research article

DOI: 10.1080/02331930500530153

Affiliations: 1: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland