Abstract
Let X be a Banach space, C be a nonempty closed convex set and \(\sigma _C\) be the support function of the set C. In this work, we give some necessary and sufficient conditions for the set C to satisfy \(\mathrm {int}(\mathrm {dom}\sigma _C)\ne \emptyset \), which enable us to study the Frechet and Gateaux differentiability of support function on the set C.
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Acknowledgements
We are grateful to Prof. C. Zalinescu for his valuable comments and analysis of earlier version of this paper, which helped us to improve the results.
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Communicated by Massoud Amini.
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Hassankhali, S., Sadeqi, I. Some Notes on the Differentiability of the Support Function. Bull. Iran. Math. Soc. 46, 1211–1222 (2020). https://doi.org/10.1007/s41980-019-00321-4
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DOI: https://doi.org/10.1007/s41980-019-00321-4