Journal of Convex Analysis 33 (2026), No. 1&2, 497--516
Copyright Heldermann Verlag 2026
Subdifferential Determination of a Primal Lower Regular Function on a Banach Space
Milen Ivanov
Radiant Life Technologies Ltd., Nicosia, Cyprus
milen@radiant-life-technologies.com
Matey Konstantinov
Faculty of Mathematics and Informatics, Sofia University, Bulgaria
matey@fmi.uni-sofia.bg
Nadia Zlateva
Faculty of Mathematics and Informatics, Sofia University, Bulgaria
zlateva@fmi.uni-sofia.bg
We generalize to Banach spaces the Thibault-Zagrodny Theorem that if f and g are primal lower regular functions and ∂f = ∂g locally, then f and g locally differ by a constant. Our method consists in a reduction to considerations of slopes.
Keywords: Primal lower regular function, slope, determination of a function.
MSC: 49J52, 47J22.
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