Related papers: A pasting lemma for Lipschitz functions
Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of of real valued Lipschitz function with non zero point-wise Lipschitz constant m-almost everywhere is residual,…
We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of the natural interpolating and sampling sequences for this space. We also find a description of the trace of such…
Given a continuous function $f: {{\mathbb R}}\to {{\mathbb R}}$ we denote the so-called "big Lip" and "little lip" functions by $ {{\mathrm {Lip}}} f$ and $ {{\mathrm {lip}}} f$ respectively}. In this paper we are interested in the…
We study functions of two variables whose sections by the lines parallel to the coordinate axis satisfy Lipschitz condition of the order $0<\a\le 1.$ We prove that if for a function $f$ the $\operatorname{Lip} \a-$ norms of these sections…
We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a…
We solve two main questions on linear structures of (non-)norm-attaining Lipschitz functions. First, we show that for every infinite metric space $M$, the set consisting of Lipschitz functions on $M$ which do not strongly attain their norm…
In this article the authors prove strong stability of the set of all Chebyshev centres of the bounded closed subset of the metric space. We endow the set of all compacts of the space $l^n_{\infty}$ with Hausdorff metric and prove that the…
If we consider a sequence of warped product length spaces, what conditions on the sequence of warping functions implies compactness of the sequence of distance functions? In particular, we want to know when a subsequence converges to a well…
We emulate the Rademacher functions on any non-commutative compact group requiring the resulting system to have pairwise disjoint spectra.
The paper shows that there is a deep structure on certain sets of bisimilar Probabilistic Automata (PA). The key prerequisite for these structures is a notion of compactness of PA. It is shown that compact bisimilar PA form lattices. These…
Given a metric space (X, d), we continue our study of the distance function x\mapsto d(x,-) and its relation to bi-Lipschitz embeddings of (X, d) into R^N. As application, given a compact metric-measure space (X, d,\mu), we give three…
In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of…
If kappa is strongly compact, lambda > kappa is regular, then (2^{< lambda})^+ --> (lambda+eta)^2_theta holds for eta,theta<kappa.
An improvement of the author's result, proved in 1961, concerning necessary and sufficient conditions for the compactness of an imbedding operator is given.
We provide sufficient conditions for a lattice polynomial function to be self-commuting. We explicitly describe self-commuting polynomial functions over chains.
The main goal of this work is to show that if two weighted homogeneous (but not homogeneous) function-germs $(\C^2,0)\to(\C,0)$ are bi-Lipschitz equivalent, in the sense that these function-germs can be included in a strongly bi-Lipschitz…
We present an alternative proof for the existence of solutions of stochastic functional differential equations satisfying a global Lipschitz condition. The proof is based on an approximation scheme in which the continuous path dependence…
We solve the following three questions concerning surjective linear isometries between spaces of Lipschitz functions $\mathrm{Lip}(X,E)$ and $\mathrm{Lip}(Y,F)$, for strictly convex normed spaces $E$ and $F$ and metric spaces $X$ and $Y$:…