Author

Dr. Fozi M. Dannan

Published in

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis 22 (January 2015) 267-277

Abstract

Inequalities play a vital role in all fields of mathematics, and they are very strong tools for investigating approximately all problems of science. In this article we established scalar and matrix generalizations of Arithmetic – Harmonic mean inequality

and Kantorovich inequality

where   . Inequalities for generalized inverse matrices has been obtained.  Exact expressions are given for the difference between the two sides of the obtained inequalities (for parallel sums and others). several examples are given to illustrate the obtained results.

Keywords. Kantorovich inequality; Arithmetic mean; Harmonic mean ; Parallel sum

; Positive de_nite matrix ; generalized inverse

Link to read full paper

http://online.watsci.org/abstract_pdf/2015v22/v22n4a-pdf/1.pdf