A Note on Ostrowski's Inequality

This paper deals with the problem of estimating the deviation of the values of a function from its mean value. We consider the following special cases: i) the case of random variables (attached to arbitrary probability fields); ii) the comparison is performed additively or multiplicatively; iii) the mean value is attached to a multiplicative averaging process

A NEW LOOK AT THE LYAPUNOV INEQUALITY

Given a Banach space E, it is proved that any function u in C2([a; b];E) verifies a Lyapunov inequality. The provided constant is sharp. Several applications are included

The Hornich-Hlawka functional inequality for functions with positive differences

We analyze the role played by $n$-convexity for the fulfillment of a series of linear functional inequalities that extend the Hornich-Hlawka functional inequality, $f\left( x\right) +f\left( y\right) +f\left( z\right) +f\left( x+y+z\right) \geq f\left( x+y\right) +f\left( y+z\right)+f\left( z+x\right) +f(0),$ including extensions to the case of positive operators.Comment: 20 page

A generalization of Lagrange's algebraic identity and connections with Jensen's inequality

We discuss a generalization of Lagrange's algebraic identity that provides valuable insights into the nature of Jensen's inequality and of many other inequalities of convexity