Related papers: Every z-linear maps is a functional p-convex

In this paper we prove that there exists a Zariski dense open subset U defined over the rationals Q in the space of all one-variable rational functions with arbitrary k poles of prescribed orders, such that for every geometric point f in…

In the paper a theorem of Piccard's type is proved and, consequently, the continuity of $\mathcal{D}$-measurable polynomial functions of $n$-th order as well as $\mathcal{D}$-measurable $n$-convex functions is shown. The paper refers to the…

The aim of the current paper is to introduce a new class of contractive mappings, which are contracting (a feature of) triangles. We prove that maps contracting triangles are continuous and give the fixed point result for such mappings. We…

We show that any function $f:\mathbb{H}^n\to\mathbb{H}$ with $f(z+c)=f(z)+c$, $z\in\mathbb{H}^n$, for some $c>0$ has a property that any limit function of a family $\{\frac{f(tz)}{t}\}_{t>0}$ when $t\to\infty$ is linear.

We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index $p$-harmonic function is a constant. For some normal subgroups of infinite index we describe a class of…

Consider the self-map F of the space of real-valued test functions on the line which takes a test function f to the test function sending a real number x to f(f(x))-f(0). We show that F is discontinuous, although its restriction to the…

In this note prove the following Berwald-type inequality, showing that for any integrable log-concave function $f:\mathbb R^n\rightarrow[0,\infty)$ and any concave function $h:L\rightarrow\mathbb [0,\infty)$, where $L$ is the epigraph of…

Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…

In this note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the…

Let $k$ be a perfect field of characteristic $p>0$, $\mathcal{V}$ a complete discrete valuation ring with residue field $k$ and field of fractions $K$ of characteristic 0, and $S$ a separated $k$-scheme of finite type. When $S$ is smooth…

The Polyak-{\L}ojasiewicz (P{\L}) condition is often invoked in nonconvex optimization because it allows fast convergence of algorithms beyond strong convexity. A function $f \colon \mathcal{M} \to \mathbb{R}$ on a Riemannian manifold…

We study the connection between cyclic quasi-monotonicity and quasi-convexity, focusing on whether every cyclically quasi-monotone (possibly multivalued) map is included in the normal cone operator of a quasi-convex function, in analogy…

A 2009 article of Allcock and Vaaler examined the vector space $\mathcal G := \overline{\mathbb Q}^\times/\overline{\mathbb Q}^\times_{\mathrm{tors}}$ over $\mathbb Q$, describing its completion with respect to the Weil height as a certain…

We discuss conditions under which a convex cone $\K\subset \R^{\Omega}$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely…

According to a 2002 theorem by Cardaliaguet and Tahraoui, an isotropic, compact and connected subset of the group $\operatorname{GL}^+(2)$ of invertible $2\times2-\,$matrices is rank-one convex if and only if it is polyconvex. In a 2005…

The zeta function of a K3 surface over a finite field satisfies a number of obvious (archimedean and l-adic) and a number of less obvious (p-adic) constraints. We consider the converse question, in the style of Honda-Tate: given a function…

We prove a Jensen-disc type theorem for polynomials $p\in\mathbb{R}[z]$ having all their zeros in a sector of the complex plane. This result is then used to prove the existence of a collection of linear operators…

In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamily of size five…

In this short note, we show that every convex, order bounded above functional on a Frechet lattice is automatically norm continuous. This improves a result in \cite{RS06} and applies to many deviation and variability measures. We also show…

Working in the p-adic analog of the complex numbers, we'll define a line integral on a small arc of a circle. This allows new versions of the Residue Theorem, the Cauchy-Goursat Theorem on discs with and without holes, Cauchy's Integral…