Related papers: Coefficient invariances of Convex functions

We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $\mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.

We study concave trace functions of several operator variables and formulate and prove multivariate generalisations of the Golden-Thompson inequality. The obtained results imply that certain functionals in quantum statistical mechanics have…

We prove a sharp moment inequality for a log-concave or a log-convex function, on Gaussian random vectors. As an application we take a stability result for the classical logarithmic Sobolev inequality of L. Gross in the case where the…

In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…

We connect the well-known theory of functional forms of variational bicomplex with the theory of antiexact differential forms. We identify antiexact functional forms as an obstruction to the variationality of differential equations. The…

In this paper, we give some definitions on quasi-convex functions and we prove inequalities contain J-quasi-convex and W-quasi-convex functions. We give also some inclusions.

We investigate several instances of the Hadamard inequality in the mean in two dimensions. As a consequence, we prove the uniqueness of minimizers of an integral functional with a polyconvex integrand, subject to mixed Dirichlet and Neumann…

In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.

We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…

We prove a sharp bound between sampling numbers and entropy numbers in the uniform norm for bounded convex sets of bounded functions.

While many bounds have been proved for partial trace inequalities over the last decades for a large variety of quantities, recent problems in quantum information theory demand sharper bounds. In this work, we study optimal bounds for…

We prove tight upper bounds for the number of vertices of a simple polygon that is the union or the intersection of two simple polygons with given numbers of convex and concave vertices. The similar question on graphs of the lower (or…

Estimates on the initial coefficients are obtained for normalized analytic functions $f$ in the open unit disk with $f$ and its inverse $g=f^{-1}$ satisfying the conditions that $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both subordinate to a…

Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value…

We give an elementary proof of a somewhat curious result, namely, that deciding whether a convex function is self-concordant is in general an intractable problem.

In this paper we establish the coefficient bodies for a wide class of families of inverse functions. We also completely describe those functions that provide boundary points of that bodies in small dimensions. As an application we get sharp…

We study the sharp constant in the Hardy inequality for fractional Sobolev spaces defined on open subsets of the Euclidean space. We first list some properties of such a constant, as well as of the associated variational problem. We then…

We prove limit relations between the sharp constants in the multivariate Bernstein-Nikolskii type inequalities for trigonometric polynomials and entire functions of exponential type with the spectrum in a centrally symmetric convex body.

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…

We provide new necessary and sufficient conditons for ensuring strong quasiconvexity in the nonsmooth case and, as a consequence, we provide a proof for the differentiable case. Furthermore, we improve the quadratic growth property for…