Related papers: New Estimates on Integral Inequalities and Their A…

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…

Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.

The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…

This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…

In this paper, we establish several new inequalities for some twice differantiable mappings. Then, we apply these inequalities to obtain new midpoint, trapezoid and perturbed trapezoid rules. Finally, some applications for special means of…

In this paper, we establish some new inequalities for class of SX(h,I) convex functions which are supermultiplicative or superadditive and nonnegative. And we also give some applications for special means.

We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null…

Classical measures of inequality use the mean as the benchmark of economic dispersion. They are not sensitive to inequality at the left tail of the distribution, where it would matter most. This paper presents a new inequality measurement…

We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of…

We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.

A new type of gradient estimate is established for diffusion semigroups on non-compact complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived for diffusion semigroups on…

The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.

Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…

In this paper, we will prove several new inequalities of Hardy's types with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and H\"older's inequality. To the best of the…

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…

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…

We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-based methodology in this setting, and discuss its basic properties. Then we point to close…

In this preprint we consider generalizations of discrete and integral Cauchy--Bunyakovskii inequalities by the method of mean values with some applications. Mostly the material is compiled as a short survey but some results are proved. Main…

We have made some new definitions using the inequalities of Young' and Nesbitt'. And we have given some features of these new definitions. After, we established new Hadamard type inequalities for convex functions in the Young and Nesbitt…