Related papers: An Inequality for Bounded Functions

In this paper, new upper and lower bounds for the Trapezoid inequality of absolutely continuous functions are obtained. Applications to some special means are provided as well.

Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…

The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya that improves Friedrichs inequality. A remarkable feature of such a proof is that…

An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.

In this note we deal with some inequalities for the tangent function that are valid for $x$ in $(-\pi/2,\pi/2)$. These inequalities are optimal in the sense that the best values of the exponents involved are obtained.

An inequality concerning ratios of gamma functions is proved. This answers a question of Guo and Qi (2003).

We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant $\delta$. The bound is expressed in the uniform entropy integral of…

In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.

In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.

We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain,…

The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…

The best approximation by bounded product functions is calculated for some very simple two-valued functions of two variables.

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.

In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…

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.

Error bounds are central objects in optimization theory and its applications. They were for a long time restricted only to the theory before becoming over the course of time a field of itself. This paper is devoted to the study of error…

In this paper, new sharp bounds for circular functions are proved. We provide some improvements of previous results by using infinite products, power series expansions and a generalisation of the so-called Bernoulli inequality. New proofs,…

We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…

We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic…