Related papers: Locally Lipschitz Functions and Bornological Deriv…

In our previous paper on this topic, we introduced the notion of k-Hessian measure associated with a continuous k-convex function in a domain \Om in Euclidean n-space, k=1,...,n, and proved a weak continuity result with respect to local…

We give a complete description of homomorphisms between two Banach algebras of Lipschitz functions with values in continuous functions. We also characterize the compactness of those homomorphisms.

This paper introduces a new notion of a Fenchel conjugate, which generalizes the classical Fenchel conjugation to functions defined on Riemannian manifolds. We investigate its properties, e.g.,~the Fenchel--Young inequality and the…

Differential forms on the Fr\'echet manifold F(S,M) of smooth functions on a compact k-dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the…

This is a follow-up of a paper by Fern\'andez-Bonder-Ritorto-Salort [8], where the classical concept of $H$-convergence was extended to fractional \(p\)-Laplace type operators. In this short paper we provide an explicit characterization of…

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his…

This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X-->V, and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a Banach space. Here, we consider the case…

In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are…

One of the classical results concerning differentiability of continuous functions states that the set $\mathcal{SD}$ of somewhere differentiable functions (i.e., functions which are differentiable at some point) is Haar-null in the space…

This paper deals with the extension of a classical theorem by R. Phelps on the G\^ateaux differentiability of Lipschitz functions on separable Banach spaces to the non-separable case. The extension of the theorem is not possible for general…

This article introduces a weak pseudo-inverse of a monotone function, which is applied to characterize the associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=t^{[-1]}(F(t(x),t(y)))$ where…

A weighted Hilbert space $F^2_{\varphi}$ of entire functions of $n$ variables is considered in the paper. The weight function $\varphi$ is a convex function on ${\mathbb C}^n$ depending on modules of variables and growing at infinity faster…

Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…

We give a simple and more elementary proof that the notions of Domain of Holomorphy and Weak Domain of Holomorphy are equivalent. This proof is based on a combination of Baire's Category Theorem and Montel's Theorem. We also obtain…

Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either has a shrinking basis or $Y$ is isomorphic to $C(2^\mathbb{N})$ and $A$ is a subset of weakly compact operators from $X$ to $Y$ which is analytic in the strong operator…

In this work, we construct a proximal average for two prox-bounded functions, which recovers the classical proximal average for two convex functions. The new proximal average transforms continuously in epi-topology from one proximal hull to…

A function $f:[a,b] \rightarrow \mathbb{R}$ is called $(p,a,b)$-convex if $f$ is $p$ times continuously differentiable, $f^{(p)}$ is convex and increasing, and $f^{(k)}(a)=0$ for all $k=1,\ldots,p$ where $f^{(j)}$ is the $j$th derivative of…

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…

We improve the rate function of McDiarmid's inequality for Hamming distance. In particular, applying our result to the separately Lipschitz functions of independent random variables, we also refine the convergence rate function of…

For a compact metric space $K$ the space $\Lip(K)$ has the Daugavet property if and only if the norm of every $f \in \Lip(K)$ is attained locally. If $K$ is a subset of an $L_p$-space, $1<p<\infty$, this is equivalent to the convexity of…