Azagra Rueda, DanielDeville, Robert2023-06-202023-06-2019970004-972710.1017/S0004972700031063https://hdl.handle.net/20.500.14352/57011Two main results presented by the authors include a mean-value inequality for a class of Gateaux subdifferentiable functions and a subdifferential Rolle’s theorem in a Banach space. For the second part, if a (Gateaux/Fréchet)subdifferentiable function f is bounded by " on the boundary of a unit ball, then there exists a Gateaux/Fréchet) subgradient of f at an interior point of the ball which is bounded by 2".engjournal articlehttp://journals.cambridge.org/action/displayJournal?jid=BAZ#open access517.98Gâteaux subdifferentialMean value inequality theoremsSubdifferential approximate Rolle's theoremFréchet subdifferentialAnálisis funcional y teoría de operadores