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Subdifferential rolle’s and mean value inequality theorems Azagra Rueda, Daniel Deville, Robert 517.98 Gâteaux subdifferential Mean value inequality theorems Subdifferential approximate Rolle's theorem Fréchet subdifferential Análisis funcional y teoría de operadores Two 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". DGICYT Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:47:26Z 2023-06-20T16:47:26Z 1997 journal article https://hdl.handle.net/20.500.14352/57011 0004-9727 10.1017/S0004972700031063 eng PB 93/0452 open access application/pdf Cambridge University Press