Related papers: A generalization of Lipschitz mappings
We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…
In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
We study generalized quasiconformal mappings in the context of the inverse Poletsky inequality. We consider the local behavior and the boundary behavior of mappings with the inverse Poletsky inequality. In particular, we obtain logarithmic…
We develop a completely bounded counterpart to the non-commutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we…
We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We…
In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary and moreover these extensions are…
In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon--Nikod\'ym property, Clarke's generalized Jacobian will be extended to this…
We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund type spaces. Consequently, we obtain new characterizations for the compactness of such…
We consider open discrete mappings of Riemannian manifolds that satisfy some modulus inequality. We investigate the possibility of a continuous extension of such mappings to an isolated point on the boundary. It is proved that, these…
Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…
We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct $\ell_1$-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free spaces over…
We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.
We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…
We study mappings with branching of a domain of Euclidean space. The H\"older and Lipschitz continuity are established for one class of spatial mappings whose characteristic satisfies the Dini type condition in a given domain. In addition,…
For a complete noncompact connected Riemannian manifold with bounded geometry, we prove the existence of isoperimetric regions in a larger space obtained by adding finitely many limit manifolds at infinity. As one of many possible…
A generalization of the triangle inequality is introduced by a mapping similar to a t-conorm mapping. This generalization leads us to a notion for which we use the $\star$-metric terminology. We are interested in the topological space…
The nonlinear concepts of mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type…
We prove in particular that the Lipschitz-free space over a finitely-dimensional normed space is complemented in its bidual. For Euclidean spaces the norm of the respective projection is $1$. As a tool to obtain the main result we establish…
If a metric subspace $M^{o}$ of an arbitrary metric space $M$ carries a doubling measure $\mu$, then there is a simultaneous linear extension of all Lipschitz functions on $M^{o}$ ranged in a Banach space to those on $M$. Moreover, the norm…