Geodesic
On two-sided unidirectional mean value inequality in a Fr\'{e}chet smooth space
Ural mathematical journal, Tome 9 (2023) no. 2, pp. 132-140

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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.
Keywords: Smooth Banach space, Fréchet subdifferential, unidirectional mean value inequality, upper limit of continuous functions. 
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     author = {Dmitry V. Khlopin},
     title = {On two-sided unidirectional mean value inequality in a {Fr\'{e}chet} smooth space},
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     url = {http://geodesic.mathdoc.fr/item/UMJ_2023_9_2_a10/}
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Dmitry V. Khlopin. On two-sided unidirectional mean value inequality in a Fr\'{e}chet smooth space. Ural mathematical journal, Tome 9 (2023) no. 2, pp. 132-140. http://geodesic.mathdoc.fr/item/UMJ_2023_9_2_a10/