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Volume 34, Issue 4
Smulyan Lemma and Differentiability of the Support Function

Ildar Sadeqi & Sima Hassankhali

Anal. Theory Appl., 34 (2018), pp. 348-357.

Published online: 2018-11

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  • Abstract

The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.

  • Keywords

Frechet and Gateaux differentiability, support function, strict convexity, Smulyan lemma.

  • AMS Subject Headings

49j50, 52A05, 52A41

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-34-348, author = {}, title = {Smulyan Lemma and Differentiability of the Support Function}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {4}, pages = {348--357}, abstract = {

The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0024}, url = {http://global-sci.org/intro/article_detail/ata/12848.html} }
TY - JOUR T1 - Smulyan Lemma and Differentiability of the Support Function JO - Analysis in Theory and Applications VL - 4 SP - 348 EP - 357 PY - 2018 DA - 2018/11 SN - 34 DO - http://doi.org/10.4208/ata.OA-2017-0024 UR - https://global-sci.org/intro/article_detail/ata/12848.html KW - Frechet and Gateaux differentiability, support function, strict convexity, Smulyan lemma. AB -

The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.

Ildar Sadeqi & Sima Hassankhali. (1970). Smulyan Lemma and Differentiability of the Support Function. Analysis in Theory and Applications. 34 (4). 348-357. doi:10.4208/ata.OA-2017-0024
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