Approximate Rolle’s theorems for the proximal subgradient and the generalized gradient

Azagra Rueda, DanielFerrera Cuesta, JuanLópez-Mesas Colomina, Fernando2023-06-202023-06-202003-07-010022-247X10.1016/S0022-247X(03)00267-1https://hdl.handle.net/20.500.14352/49793We establish approximate Rolle's theorems for the proximal subgradient and for the generalized gradient. We also show that an exact Rolle's theorem for the generalized gradient is completely false in all infinite-dimensional Banach spaces (even when they do not possess smooth bump functions).engApproximate Rolle’s theorems for the proximal subgradient and the generalized gradientjournal articlehttp://www.sciencedirect.com/science/journal/0022247Xopen access517.98Rolle theoremProximinal subspaceGeneralized gradientAnálisis matemático1202 Análisis y Análisis Funcional