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The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…
Let $X$ be a compact subset of the complex plane and $x \in X$. A necessary and sufficient condition is given in terms of Hausdorff contents for the existence of a bounded point derivation at $x$ on the space of vanishing Campanato…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…
This article examines differentiability properties of the value function of positioning choice problems, a class of optimisation problems in finite-dimensional Euclidean spaces. We show that positioning choice problems' value function is…
Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…
It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if…
Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some regularity conditions. Unlike the univariate case, the converse also requires regularity…
In this paper, we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to ${\bf L}^1$-distance.
We consider Borwein-Preiss and Ekeland variational principles using distance functions that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
The concept of rotation symmetric functions from the Boolean domain is extended to the multiple-valued (MV) domain. It is shown that symmetric functions are a subset of the rotation symmetric functions. Functions exhibiting these kinds of…
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
We introduce an adaptation of integral approximation operators to set-valued functions (SVFs, multifunctions), mapping a compact interval $[a,b]$ into the space of compact non-empty subsets of ${\mathbb R}^d$. All operators are adapted by…
Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant…
In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. These fractional derivatives lead to non-symmetric boundary value…
Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set $F(t,x)$. Certain properties of state trajectories can be derived when, in addition to other…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
Let $T\subset\mathbb{R}$, $M$ be a metric space with metric $d$, and $M^T$ be the set of all functions mapping $T$ into $M$. Given $f\in M^T$, we study the properties of the approximate variation $\{V_\varepsilon(f)\}_{\varepsilon>0}$,…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…