Related papers: Strong Forms of Weakly e-continuous Functions

This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A…

We introduce a notion of a weak elementary fibration and prove that it does exist in certain interesting cases. Our notion is a modification of the M. Artin's notion of an elementary fibration.

There is a useful counterpart of conformal prediction for e-values, called conformal e-prediction. Conformal prediction can serve as basis for testing the assumption of exchangeability, leading to conformal testing. Similarly, conformal…

The notion of weakly monotone functions extends the classical definition of monotone function, that can be traced back to H.Lebesgue. It was introduced, in the setting of Sobolev spaces, by J.Manfredi, and thoroughly investigated in the…

The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…

We prove a strong non-structure theorem for a class of metric structures with an unstable pair of formulae. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies several…

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and…

We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…

Lower semi-continuity (\texttt{LSC}) is a critical assumption in many foundational optimisation theory results; however, in many cases, \texttt{LSC} is stronger than necessary. This has led to the introduction of numerous weaker continuity…

The notion of ordinal concavity of utility functions has recently been considered by Hafalir, Kojima, Yenmez, and Yokote in economics while there exist earlier related works in discrete optimization and operations research. In the present…

We introduce three classes of analytic functions with fixed second coefficient which are defined using the class $\mathcal{P}$ of analytic functions with positive real part. The objective is to determine radii such that the three classes…

Weakly stable torsion classes were introduced by the author and Yekutieli to provide a torsion theoretic characterisation of the notion of weak proregularity from commutative algebra. In this paper we investigate weakly stable torsion…

It is perhaps not widely recognized that certain common notions of distance between probability measures have an alternative dual interpretation which compares corresponding functionals against suitable families of test functions. This dual…

In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.…

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…

This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using…

In this paper we introduce a weak version of level and epigraph convergence for level functions on topological spaces. In the particular case of topological groups we are able to define convolutions in the set of level functions and show…

This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…