Related papers: Equivalent inequalities

We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.

We shall give a refinement of the arithmetic-geometric mean inequality.

In this paper we give necessary and sufficient conditions for the equality case in Wielandt's eigenvalue inequality.

Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.

We obtain variational inequalities for some classes of bilinear averages of one variable, generalizing the variational inequalities for averages of R. Jones {\it et al}. As an application we get almost everywhere convergence for the ergodic…

In this article we discuss a generalized Wirtinger inequality.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…

We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.

We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…

The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.

In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.

In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions,…

In this paper, we prove some inequalities for the differences and ratios of the beta function.

Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.

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.

The equivalence of multidimensional systems is closely related to the reduction of multivariate polynomial matrices, with the Smith normal form of matrices playing a key role. So far, the problem of reducing multivariate polynomial matrices…

The notion of equivalence of maximally entangled bases of bipartite d-dimensional Hilbert spaces is introduced. An explicit method of inequivalent bases construction is presented.

The notion of different kind of algebraic Casorati curvatures are introduced. Some results expressing basic Casorati inequalities for algebraic Casorati curvatures are presented. Equality cases are also discussed. As a simple application,…

In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.