An integral inequality for convex functions defined on linear spaces is obtained which contains in a particular case a refinement for the first part of the celebrated HermiteHadamard inequality. Applications for semi-inner products on normed linear spaces are also provided.

The Schur-convexity at the upper and lower limits of the integral for the mean of a convex function is researched. As applications, a form with a parameter of Stolarsky’s mean is obtained and a relevant double inequality that is an extension of a known inequality is established. © 2009 Elsevier Ltd. All rights reserved.

The main purpose of this paper is to use a Grüss type inequality for RiemannStieltjes integrals to obtain a sharp integral inequality of Ostrowski-Grüss type for functions whose first derivative are functions of Lipschitizian type and precisely characterize the functions for which equality holds.

We establish an integral formula on a smooth, precompact domain in a Kahler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula we prove an isoperimetric inequality in terms of a positive lower bound for the Hermitian curvature of the boundary. Combining with a Minkowski type formula on the complex hyperbolic space we prove that any closed, embedde...

This paper presents a generalization of Young’s inequality to the real functions of several variables. Moreover, the relevant facts about Young’s inequality and its extension including improved proofs are provided in a review. The basic results are initiated by applying the integral method to a strictly increasing continuous function of one variable. c ©2016 All rights reserved.

The paper addresses the stability problem of linear time delay system. In the literature, the most popular approach to tackle this problem relies on the use of LyapunovKrasovskii functionals. Many results have proposed new functionals and techniques for deriving less and less conservative stability conditions. Nevertheless, all these approaches use the same trick, the well-known Jensen’s inequa...

In this paper we study the inequalities of the determinants of the positive definite matrices and the invertible matrices by applying the integral method and matrix theory such that extensions of Fan Ky’s inequality are established. And then an improvement of Fan Ky’s inequality is given by using the positive definiteness of Gram matrix. Mathematics Subject Classification (2010): 15A15, 26D15.

Chebyshev’s integral inequality, also known as the covariance inequality, is an important problem in economics, finance, and decision making. In this paper we derive some covariance inequalities for monotonic and non-monotonic functions. The results developed in our paper could be useful in many applications in economics, finance, and decision making.

In this paper, we give a unified generalization of Aczél, Popoviciu and Bellman's inequalities. The result is then applied to deriving a refinement of Aczél's inequality and Bellman's inequality. As consequences, several interesting integral inequalities of Aczél-Popoviciu-Bellman type are obtained.

We give a short summary of Varopoulos’ generalised Hardy-LittlewoodSobolev inequality for self-adjoint C0 semigroups and give a new probabilistic representation of the classical fractional integral operators on Rn as projections of martingale transforms. Using this formula we derive a new proof of the classical Hardy-LittlewoodSobolev inequality based on Burkholder-Gundy and Doob’s inequalities...