Related papers: Functions with strictly convex epigraph
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
In this paper we provide an efficient computation of the projection onto the cone generated by the epigraph of the perspective of any convex lower semicontinuous function. Our formula requires solving only two scalar equations involving the…
The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $\Omega$ of a locally convex space $X$ and taking values in a locally convex space…
We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.
In this paper our aim is to deduce some sufficient (and necessary) conditions for the close-to-convexity of some special functions and their derivatives, like Bessel functions, Struve functions, and a particular case of Lommel functions of…
It is shown that if the squeezing function tends to one at an h-extendible boundary point of a $\mathcal C^\infty$-smooth, bounded pseudoconvex domain, then the point is strictly pseudoconvex.
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable…
We study the boundary regularity of proper holomorphic mappings between strictly pseudoconvex domains with $C^2$-boundaries.
We prove conditions for the existence of a continuous linear right inverse for a surjective convolution operator in spaces of germs of analytic functions on convex subsets of the complex plane. Considered convex sets have a countable…
We show that the existence of a function in $L^{1}$ with constant geodesic X-ray transform imposes geometrical restrictions on the manifold. The boundary of the manifold has to be umbilical and in the case of a strictly convex Euclidean…
A real valued function $f$ defined on a convex $K$ is anemconvex function iff it satisfies $$ f((x+y)/2) \le (f(x)+f(y))/2 + 1. $$ A thorough study of approximately convex functions is made. The principal results are a sharp universal upper…
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
We give a relation between verbatim generating functions of what we call Pythagorean languages and matrix convexity. Namely, several multivariate matrix convex functions occurring in the existing matrix analysis literature arise naturally…
Previously, we have systematically constructed explicit real algebraic functions which are represented as the compositions of smooth real algebraic maps whose images are domains surrounded by hypersurfaces of degree 1 or 2 with canonical…
Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms…
In this paper, approximate convexity and approximate midconvexity properties, called $\varphi$-convexity and $\varphi$-midconvexity, of real valued function are investigated. Various characterizations of $\varphi$-convex and…
This article explores anti-coproximinal and strongly anti-coproximinal subspaces in the spaces of vector-valued continuous functions and operator spaces. We provide a complete characterization of strongly anti-coproximinal subspaces in $…
We study the contraction of strictly convex, axially symmetric hypersurfaces by a non-symmetric, non-homogeneous, fully nonlinear function of curvature. Starting from axially symmetric hypersurfaces with even profile curves, we show…