Abstract
We study the problem of extending continuous quasiconvex real-valued functions from a subspace of a real normed linear space. Our results are essentially finite-dimensional and are based on a technical lemma which permits to “extend” a nested family of open convex subsets of a given subspace to a nested family of open convex sets in the whole space, in such a way that certain topological conditions are satisfied.
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Acknowledgements
The research of the author is partially supported by GNAMPA-INdAM, Project GNAMPA 2020. The author would like to thank M. Bianchi, E. Miglierina, and R. Pini for many discussions on the subject and for useful comments and remarks that helped him in preparing this paper.
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Communicated by Nicolas Hadjisavvas.
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De Bernardi, C.A. On the Extension of Continuous Quasiconvex Functions. J Optim Theory Appl 187, 421–430 (2020). https://doi.org/10.1007/s10957-020-01767-x
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DOI: https://doi.org/10.1007/s10957-020-01767-x