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Hahn–Banach extension theorems for multifunctions revisited

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  • C. Zălinescu

Abstract

Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing results. Then we derive the Yang extension theorem using a similar proof as well as a stronger version of it using a classical separation theorem. Moreover, we give counterexamples to several extension theorems stated in the literature. Copyright Springer-Verlag 2008

Suggested Citation

  • C. Zălinescu, 2008. "Hahn–Banach extension theorems for multifunctions revisited," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 493-508, December.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:3:p:493-508
    DOI: 10.1007/s00186-007-0193-6
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