Related papers: Coderivatives at infinity of set-valued mappings

In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…

The fundamental result of Li, Long, and Srinivasan on approximations of set systems has become a key tool across several communities such as learning theory, algorithms, computational geometry, combinatorics and data analysis. The goal of…

The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all $L^2$-based…

We prove an embedded local uniformization theroem for a valuation centered on a point of a quasi-excellent scheme of characteristic zero. The proof reduces to valuations of rank 1 and consists in desingularizing the ideal formed by the…

We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of roots of unity.

In this paper, we study Frechet derivatives and Mordukhovich derivatives (or coderivatives) of single-valued mappings in Euclidean spaces. At first, we prove the guideline for calculating the Frechet derivatives of single-valued mappings by…

One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…

Rademacher theorem asserts that Lipschitz continuous functions between Euclidean spaces are differentiable almost everywhere. In this work we extend this result to set-valued maps using an adequate notion of set-valued differentiability…

A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…

We introduce a large scale analogue of the classical fixed-point property for continuous maps, which shall apply to coarse maps. We also develop a coarse version of degree for coarse maps on Euclidean spaces. Then, applying a coarse…

We propose a level proximal subdifferential for a proper lower semicontinuous function. Level proximal subdifferential is a uniform refinement of the well-known proximal subdifferential, and has the pleasant feature that its resolvent…

In this paper we introduce and study the concept of set extremality for systems of convex sets in vector spaces without topological structures. Characterizations of the extremal systems of sets are obtained in the form of the convex…

The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mapping in Hausdorff p-vector spaces, and the fixed point theorem for upper semicontinuous set-valued mappings in Hausdorff locally…

We study additive double character sums over two subsets of a finite field. We show that if there is a suitable rational self-map of small degree of a set $D$, then this set contains a large subset $U$ for which the standard bound on the…

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the…

An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-called residuations. Based on this,…

In this study, multivalued generalizations of certain classes of single-valued transformations defined on metric spaces are obtained. Building upon recently introduced concepts such as mappings contracting perimeters of triangles, new…

An integer-valued fixed point index for compositions of acyclic multivalued maps is constructed. This integer-valued fixed point index has the properties: additivity, homotoy invariance, normalization, commutativity, multiplicativity. The…

A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…

Optimal zero-delay coding (quantization) of $\mathbb{R}^d$-valued linearly generated Markov sources is studied under quadratic distortion. The structure and existence of deterministic and stationary coding policies that are optimal for the…