A metric tangential calculus.
A new proof of Fréchet differentiability of Lipschitz functions
We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the closure of the set of its points of Gâteaux differentiability is norm separable.
A note on Banach spaces and sub differentials of convex functions
A Note on Differentiability of Lipschitz Maps
We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
A note on geometric characterization of Fréchet differentiability
A note on intermediate differentiability of Lipschitz functions
Let be a Lipschitz function on a superreflexive Banach space . We prove that then the set of points of at which has no intermediate derivative is not only a first category set (which was proved by M. Fabian and D. Preiss for much more general spaces ), but it is even -porous in a rather strong sense. In fact, we prove the result even for a stronger notion of uniform intermediate derivative which was defined by J.R. Giles and S. Sciffer.
A Note on Right-Equivalence of Map-Germs.
A note on singular points of convex functions in Banach spaces
A note on strong differentiability spaces
A note on the inverse function theorem of Nash and Moser.
A Note on the Order of Determination of a Finitely Determined Germ.
A one-sided version of Alexiewicz-Orlicz's differentiability theorem.
Modificando adecuadamente el método de un trabajo olvidado [1], probamos que si una aplicación continua, de un subconjunto abierto no vacío U de un espacio vectorial topológico metrizable separable y de Baire E, en un espacio localmente convexo, es direccionalmente diferenciable por la derecha en U según un subconjunto comagro de E, entonces, es genéricamente Gâteaux diferenciable en U. Nuestro resultado implica que cualquier espacio vectorial topológico, metrizable, separable y de Baire, es débilmente...
A partial solution for Feynman's problem – a new derivation of the Weyl equation.
A proof of the inverse function theorem
A rank theorem for analytic maps between power series spaces
A regularity lemma for functions of several variables.
We shall prove the following Theorem. Let Fs and Fu be two continuous transverse foliations with uniformly smooth leaves, of some manifold. If f is uniformly smooth along the leaves of Fs and Fu, then f is smooth.
A Relation Between Growth and the Spectrum of the Laplacian.
A remark on small divisors problems
A semi-global Taylor formula for manifolds
A set of axioms for the degree of a tangent vector field on differentiable manifolds.