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Affine selections of convex set-valued functions

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Summary

It is shown that every convex set-valued function defined on a cone with a cone-basis in a real linear space with compact values in a real locally convex space has an affine selection. Similar results can be obtained for midconvex set-valued functions.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Pedagogical University, Podchorążych 2, PL-30-084, Krakow, Poland

    Andrzej Smajdor & Wilhelmina Smajdor

  2. Institute of Mathematics, Silesian University, Bankowa 14, PL-40-007, Katowice, Poland

    Andrzej Smajdor & Wilhelmina Smajdor

Authors
  1. Andrzej Smajdor
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  2. Wilhelmina Smajdor
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Smajdor, A., Smajdor, W. Affine selections of convex set-valued functions. Aeq. Math. 51, 12–20 (1996). https://doi.org/10.1007/BF01831137

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  • DOI: https://doi.org/10.1007/BF01831137

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