Related papers: Approximations and Lipschitz continuity in p-adic …
For a function $f$ that is piecewise analytic on a quasi-smooth arc $\mathcal{L}$ and any $0<\sigma<1$ we construct a sequence of "near-best" polynomials that converge at a rate $e^{-n^{\sigma}}$ at each point of analyticity of $f$ and are…
We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…
In this article, we study the Lipschitz Geometry at infinity of complex analytic sets and we obtain results on algebraicity of analytic sets and on Bernstein's problem. Moser's Bernstein Theorem says that a minimal hypersurface which is a…
We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.
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…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We prove that every local derivation on a complex semisimple finite-dimensional Leibniz algebra is a derivation.
In Euclidean space of dimension 2 or 3, we study a minimum time problem associated with a system of real-analytic vector fields satisfying H\"ormander's bracket generating condition, where the target is a nonempty closed set. We show that,…
We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…
The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $\sigma$-compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled.…
We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…
We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such…
The $p$-modulus of curves, test plans, upper gradients, charts, differentials, approximations in energy and density of directions are all concepts associated to the theory of Sobolev functions in metric measure spaces. The purpose of this…
Recent research has shown that piecewise smooth (PS) functions can be approximated by piecewise linear functions with second order error in the distance to a given reference point. A semismooth Newton type algorithm based on successive…
In this note, we establish the Lipschitz continuity of finite-dimensional globally convex functions on all given balls and global Lipschitz continuity for eligible functions of that type. The Lipschitz constants in both situations draw…
We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a small set similar to Lusin's theorem. Previous results could…
We show that for each fixed non-constant complex polynomial $P$ of the plane there exists a homeomorphism $h$ such that $P\circ h$ is a Lipschitz quotient mapping. This corrects errors in the construction given earlier by Johnson et. al.…
We characterize cofinally Bourbaki quasi-complete metric spaces and their completions in terms of certain Lipschitz-type functions. To this end, we introduce and study a new class of functions, namely strongly uniformly locally Lipschitz…
Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, where "almost everywhere" refers to the Lebesgue measure. In this paper we prove a differentiability result of similar type,…
We provide comparison principles for convex functions through its proximal mappings. Consequently, we prove that the norm of the proximal operator determines a convex the function up to a constant. A new characterization of Lipschitzianity…