Inequalities for Convex Functions on Simplexes and Their Cones

The aim of this paper is to present the fundamental inequalities for convex functions on Euclidean spaces. The work is based on the geometry of the simplest convex sets and properties of convex functions. Some obtained inequalities are applied to demonstrate a natural way of generalizing the Hermite-Hadamard inequality

Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions

We establish a Fejér type inequality for harmonically convex functions. Our results are the generalizations of some known results. Moreover, some properties of the mappings in connection with Hermite-Hadamard and Fejér type inequalities for harmonically convex functions are also considered

A Bauer-Hausdorff Matrix Inequality

We present a biorthogonal process for two subspaces of C . Applying this process, we derive a matrix inequality, which generalizes the Bauer-Hausdorff inequality for vectors and includes the Wang-IP inequality for matrices. Meanwhile, we obtain its equivalent matrix inequality

Convex Combination Inequalities of the Line and Plane

The paper deals with convex combinations, convex functions, and Jensen’s functionals. The main idea of this work is to present the given convex combination by using two other convex combinations with minimal number of points. For example, as regards the presentation of the planar combination, we use two trinomial combinations. Generalizations to higher dimensions are also considered

Improvement of Aczél's Inequality and Popoviciu's Inequality

We generalize and sharpen Aczél's inequality and Popoviciu's inequality by means of two classical inequalities, a unified improvement of Aczél's inequality and Popoviciu's inequality is given. As application, an integral inequality of Aczél-Popoviciu type is established

A Bauer-Hausdorff Matrix Inequality

We present a biorthogonal process for two subspaces of ℂn. Applying this process, we derive a matrix inequality, which generalizes the Bauer-Hausdorff inequality for vectors and includes the Wang-IP inequality for matrices. Meanwhile, we obtain its equivalent matrix inequality