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.
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Dedicated to Jean-Paul Penot with the occasion of his retirement.
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Zălinescu, C. Hahn–Banach extension theorems for multifunctions revisited. Math Meth Oper Res 68, 493–508 (2008). https://doi.org/10.1007/s00186-007-0193-6
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DOI: https://doi.org/10.1007/s00186-007-0193-6