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Journal of Convex Analysis 30 (2023), No. 4, 1351--1378
Copyright Heldermann Verlag 2023

Properties of the Fréchet Derivative of the Fenchel Conjugate of the Antidistance Function

Dariusz Zagrodny
Faculty of Mathematics and Computer Science, University of Lodz, Poland

The Fréchet derivative of the Fenchel conjugate of the antidistance function is locally Lipschitz in the Hilbert space setting. It is shown that the Gâteaux differential of the operator, at points of the existence, is bounded self-adjoint operator (it is symmetric everywhere defined on the Hilbert space). Assuming Gâteaux or Fréchet differentiability of the operator results on the strong convergence of subgradients along some arcs are also provided.

Keywords: Antidistance function, subdifferentials, subgradients, Gateaux derivative, Frechet derivative.

MSC: 49J52.

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