Related papers: On Khintchine inequalities with a weight
We use different approaches to study a generalization of a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type…
In this expository article we introduce a diagrammatic scheme to represent reverse classes of weights and some of their properties.
In this paper we study two different weighted isoperimetric inequalities. In the first part of the paper we prove a sharp stability result for the isoperimetric inequality with a log-convex weight. In the second part we analize the behavior…
We obtain some inequalities which are stronger than the Schur majorization inequalities.
In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…
We prove a variation of Gronwall's lemma.
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some applications in different abstract spaces and obtain some new interesting…
This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are…
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We derive the exponential as well as power decreasing tail estimations for normed sums of centered independent identical distributed (or not) random variables on the Khintchine's form. We consider arbitrary, in particular, non-Rademacher's…
In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.
In the paper we provide measure estimates for the set of numbers whose sequence of products of continued fraction partial quotients $M_n = a_1 \ldots a_n$ has exponential growth with rate close to the one predicted by Khintchine's theorem,…
In this paper we consider a weighted version of one dimensional discrete Hardy's Inequality on half-line with power weights of the form $n^\alpha$. Namely we consider: \begin{equation} \sum_{n=1}^\infty |u(n)-u(n-1)|^2 n^\alpha \geq…
A simple proof of the weighted two variable geometric-arithmetic a mean inequality based on one given earlier valid only for integer weights
An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.
Using double counting, we prove Delsarte inequalities for $q$-ary codes and their improvements. Applying the same technique to $q$-ary constant-weight codes, we obtain new inequalities for $q$-ary constant-weight codes.
In this short paper we prove a quantitative version of the Khintchine-Groshev Theorem with congruence conditions. Our argument relies on a classical argument of Schmidt on counting generic lattice points, which in turn relies on a certain…
Derksen and Weyman described the cone of semi-invariants associated with a quiver. We give an inductive description of this cone, followed by an example of refinement of the inequalities characterising anti-invariant weights in the case of…
The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.