Examples of convex functions and classifications of normed spaces.
Existence and stability of measure differential equations
Extension of smooth functions in infinite dimensions, I: unions of convex sets
Let f be a smooth function defined on a finite union U of open convex sets in a locally convex Lindelöf space E. If, for every x ∈ U, the restriction of f to a suitable neighbourhood of x admits a smooth extension to the whole of E, then the restriction of f to a union of convex sets that is strictly smaller than U also admits a smooth extension to the whole of E.
Fenchel-Orlicz spaces [Book]
Flett's mean value theorem in topological vector spaces.
Fonction convexe d'une mesure et applications
Fonctions convexes de première classe.
Fonctions dérivables
Fonctions mesurables et *-scalairement mesurables, mesures banachiques majorées, martingales banachiques, et propriété de Radon-Nikodym
Fréchet differentiability of Lipschitz functions via a variational principle
Fréchet differentiability, strict differentiability and subdifferentiability
Fréchet differentiability via partial Fréchet differentiability
Let be Banach spaces and a real function on . Let be the set of all points at which is partially Fréchet differentiable but is not Fréchet differentiable. Our results imply that if are Asplund spaces and is continuous (respectively Lipschitz) on , then is a first category set (respectively a -upper porous set). We also prove that if , are separable Banach spaces and is a Lipschitz mapping, then there exists a -upper porous set such that is Fréchet differentiable at every...
Fréchet directional differentiability and Fréchet differentiability
Zaj’ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any real-valued function on a normed linear space, the set of points where the function is Fréchet directionally differentiable but not Fréchet differentiable...
Functions of finite fractional variation and their applications to fractional impulsive equations
We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.
Fundamental theorem of Wiener calculus.
Gâteaux derivative and orthogonality in -classes.
Gâteaux differentiability for functionals of type Orlicz-Lorentz.
Gâteaux differentiable functions are somewhere Fréchet differentiable
Gateaux Differentials in Banach Algebras.
Gâteaux smooth partitions of unity on weakly compactly generated Banach spaces