Shoshana Abramovich

More about Hermite-Hadamard inequalities, Cauchy's means, and superquadracity.

New results associated with Hermite-Hadamard inequalities for superquadratic functions are given. A set of Cauchys type means is derived from these Hermite-Hadamard-type inequalities, and its log-convexity and monotonicity are proved.

Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 3

For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest.

Normalized Jensen Functional, Superquadracity and Related Inequalities

In this paper we generalize the inequality

Generalizations of Jensen-Steffensen and related integral inequalities for superquadratic functions

MJ_n (f,x,q) \geqslant J_n (f,x,p) \geqslant mJ_n (f,x,q)

On the behavior of the solutions of y″ + p(x)y = ƒ(x)

where

The Behavior of the Difference Between Two Means

J_n (f,x,p) = \sum\limits_{i = 1}^n {p_i f(x_i ) - f\left( {\sum\limits_{i = 1}^n {p_i x_i } } \right)} ,