We study metric spheres ( Z , d ) $(Z, d_{Z} )$ obtained by gluing two hemispheres of S 2 $\mathbb {S}^{2}$ along an orientation-preserving homeomorphism g : 1 → $g \colon \mathbb {S}^{1} \rightarrow {S}^{1}$ where $d_{Z}$ is the canonical distance that locally isometric to off seam. show if quasiconformally equivalent in geometric sense, then $g$ a welding with conformally removable curves. al...

We study a notion of an equivariant, Lipschitz, permutationinvariant centroid for triples of points in mapping class groups MCG(S), which satisfies a certain polynomial growth bound. A consequence (via work of Druţu-Sapir or Chatterji-Ruane) is the Rapid Decay Property for MCG(S).

Based on the notion of relativemaximalmonotonicity, a hybrid proximal point algorithm is introduced and then it is applied to the approximation solvability of a general class of variational inclusion problems, while achieving a linear convergence. The obtained results generalize the celebrated work of Rockafellar (1976) where the Lipschitz continuity at 0 of the inverse of the set-valued mappin...

Let X, Y be the normed spaces, C ⊂ X a convex set, and T : C → Y a continuous mapping. Some weak conditions implying the Lipschitz continuity of T are presented. Applications to the fixed point theory and theory of composition operators are presented.

We investigate the paramater of the average range of M Lipschitz mapping of a given graph. We focus on well-known classes such as paths, complete graphs, complete bipartite graphs and cycles and show closed formulas for computing this parameter and also we conclude asymptotics of this parameter on these aforementioned classes.

In this work, we use a notion of convexificator [25] together with the support function [3, 4, 15, 16, 41] to establish necessary optimality conditions for set valued bilevel optimization problems. Fortunately, the Lipschitz property of a set-valued mapping is conserved for its support function. An intermediate set-valued optimization problem is introduced to help us in our investigation.

We show that the gradient mapping of the squared norm of Fischer-Burmeister function is globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving nonlinear second order cone complementarity problems via the conjugate gradient method and the semismooth Newton’s method.

Many theoretical results in the machine learning domain stand only for functions that are Lipschitz continuous. Lipschitz continuity is a strong form of continuity that linearly bounds the variations of a function. In this paper, we derive tight Lipschitz constants for two families of metrics: Mahalanobis distances and bounded-space bilinear forms. To our knowledge , this is the first time the ...

In this paper‎, ‎using a generalized Dunkl translation operator‎, ‎we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the$(psi,p)$-Lipschitz Dunkl condition in the space $mathrm{L}_{p,alpha}=mathrm{L}^{p}(mathbb{R},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.  

Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.