On two-sided unidirectional mean value inequality in a Fréchet smooth space

Dmitry V. Khlopin

Ural mathematical journal, Tome 9 (2023) no. 2, pp. 132-140

Résumé

The paper is devoted to a new unidirectional mean value inequality for the Fréchet subdifferential of a continuous function. This mean value inequality finds an intermediate point and localizes its value both from above and from below; for this reason, the inequality is called two-sided. The inequality is considered for a continuous function defined on a Fréchet smooth space. This class of Banach spaces includes the case of a reflexive space and the case of a separable Asplund space. As some application of these inequalities, we give an upper estimate for the Fréchet subdifferential of the upper limit of continuous functions defined on a reflexive space.

Détail

Keywords: Smooth Banach space, unidirectional mean value inequality, upper limit of continuous functions.
Mots-clés : Fréchet subdifferential

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