Related papers: On affine selections of set-valued functions
The mean value theorem of calculus states that, given a differentiable function $f$ on an interval $[a, b]$, there exists at least one mean value abscissa $c$ such that the slope of the tangent line at $c$ is equal to the slope of the…
The main purpose of this paper is to determine the solution of generalized convex set-valued mappings satisfying certain functional equation. Some conclusions of stability of set-valued functional equations are obtained.
This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges…
In this work, we will present variants Fixed Point Theorem for the affine and classical contexts, as a consequence of general Brouwer's Fixed Point Theorem. For instance, the affine results will allow working on affine balls, which are…
In the paper, we introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen inequality and…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
We study the relationship between many natural conditions that one can put on a diffeological vector space: being fine or projective, having enough smooth (or smooth linear) functionals to separate points, having a diffeology determined by…
In this paper, we develop new affine-invariant algorithms for solving composite convex minimization problems with bounded domain. We present a general framework of Contracting-Point methods, which solve at each iteration an auxiliary…
This work provides formulae for the $\epsilon$-subdifferential of integral functions in the framework of complete $\sigma$-finite measure spaces and locally convex spaces. In this work we present here new formulae for this…
How small can a set be while containing many configurations? Following up on earlier work of Erd\H os and Kakutani \cite{MR0089886}, M\'ath\'e \cite{MR2822418} and Molter and Yavicoli \cite{Molter}, we address the question in two…
We prove a result on the relationship between the relative conormal space of an analytic function $f$ on affine space and the relative conormal space of $f$ restricted to a hyperplane slice, at a point where the relative conormal space of…
The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function outside the interval. In a previous paper we discussed the…
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
In this paper we show that an affine space is determined by the abstract group structure of its group of regular automorphisms in the category of connected affine varieties. To prove this we study commutative subgroups of the group of…
We investigate Baire classes of strongly affine mappings with values in Fr\'echet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki's result on affine functions of the first Baire class is related to 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…
Let $S$ be a finite set with $n$ elements in a real linear space. Let $\cJ_S$ be a set of $n$ intervals in $\nR$. We introduce a convex operator $\co(S,\cJ_S)$ which generalizes the familiar concepts of the convex hull $\conv S$ and the…
We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…
We show that in a metric space, any continuous function with compact sublevel sets and finite metric slope is uniquely determined by the slope and its critical values.