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math.FA2010
On some problems on smooth approximation and smooth extension of Lipschitz functions on Banach-Finsler Manifolds
M. Jimenez-Sevilla, L. Sanchez-Gonzalez
Let us consider a Riemannian manifold (either separable or non-separable). We prove that, for every , every Lipschitz function can be uniformly a…
math.FA2005
Approximation by smooth functions with no critical points on separable Banach spaces
D. Azagra, M. Jimenez-Sevilla
We characterize the class of separable Banach spaces such that for every continuous function and for every continuous function the…
math.FA2000
Rolle's theorem is either false or trivial in infinite-dimensional Banach spaces
Daniel Azagra, Mar Jimenez-Sevilla
We prove the following new characterization of (Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space has a smooth (Lipschitz) bump function…