Related papers: Some inequalities for tetrahedra

This paper describes the analysis of Lagrange interpolation errors on tetrahedrons. In many textbooks, the error analysis of Lagrange interpolation is conducted under geometric assumptions such as shape regularity or the (generalized)…

We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.

We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…

We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. We show that if the pinching condion is strong enough with a dependance on the norm of the second foundamental form, then the hypersurface is…

In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.

In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.

In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of…

We address ZFC inequalities between some cardinal invariants of the continuum, which turned to be true in spite of strong expectations given by [RoSh:470].

We prove a relative isoperimetric inequalities for Lagrangian half disks in $\mathbb{C}^2$ with respect to a Lagrangian plane, or a complex plane, or a union of any two of Lagrangian or complex planes that intersect transversally at the…

Kinser developed a hierarchy of inequalities dealing with the dimensions of certain spaces constructed from a given quantity of subspaces. These inequalities can be applied to the rank function of a matroid, a geometric object concerned…

Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.

In the paper, by using Lupa\c{s} integral inequality, the authors find some new inequalities for the complete elliptic integrals of the first and second kinds. These results improve some known inequalities.

In this paper, we prove some new inequalities of Hadamard-type for convex functions on the co-ordinates.

[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…

In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which…

We present three non-equivalent procedures to obtain entwining (non-constant) tetrahedron maps. Given a tetrahedron map, the first procedure incorporates its underlying symmetry group. With the second procedure we obtain several classes of…

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third side as diameter. In particular, we find…

In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…

Our main result is that every n-dimensional polytope can be described by at most (2n-1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound…