93 research outputs found
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 -convexity for the fulfillment of a series
of linear functional inequalities that extend the Hornich-Hlawka functional
inequality, 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
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