Generic differentiability of mappings and convex functions in Banach and locally convex spaces
How to define "convex functions" on differentiable manifolds
In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: . if M is a linear manifold, then (M) contains convex functions, . (·) is invariant under diffeomorphisms, . each f ∈ (M) is differentiable on a dense -set, is investigated.
Implicit functions from locally convex spaces to Banach spaces
We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller -map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.
Infinite Dimensional Calculus Allowing Nonconvey Domains with Empty Interior.
Isometric Differentiable Functions on Real Normed Space
In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.
-continuous partitions of unity on normed spaces
Lectures on maximal monotone operators.
These lectures will focus on those properties of maximal monotone operators which are valid in arbitrary real Banach spaces.
Lie derivatives of sectorform fields
M-holomorfne funkcije
Minimizing Harmonic Mappings form a surface perfored with small holes into a riemannian manifold.
Necessary Conditions for Multiple Integral Problem in the Calculus of Variations.
Norm Derivatives on Spaces of Operators.
Notes on differential calculus in topological liear spaces.
On Asplund functions
A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.
On collective compactness of derivatives
On conability of singlevalued mappings
On Hadamard differentiability
On inverses of -convex mappings
In the first part of this paper, we prove that in a sense the class of bi-Lipschitz -convex mappings, whose inverses are locally -convex, is stable under finite-dimensional -convex perturbations. In the second part, we construct two -convex mappings from onto , which are both bi-Lipschitz and their inverses are nowhere locally -convex. The second mapping, whose construction is more complicated, has an invertible strict derivative at . These mappings show that for (locally) -convex mappings...
On Lipschitz and d.c. surfaces of finite codimension in a Banach space
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated -ideals are studied. These -ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.
On local convexity of nonlinear mappings between Banach spaces
We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.