Results in Mathematics

, Volume 72, Issue 3, pp 1315–1328 | Cite as

Piecewise Quadratic Interpolation and Applications to the Young Inequality

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Abstract

Polynomial interpolation has been used for centuries to find approximate values of a function, then to find related quantities like integrals and derivatives. In this article, we present a completely new application of polynomial interpolation. More precisely, we implement an inductive quadratic interpolation formula to obtain refinements and reverses of Young’s inequality for numbers and matrices. The matrices applications include determinants and ordering inequalities.

Keywords

Polynomial interpolation Positive matrices Matrix means 

Mathematics Subject Classification

15A39 15B48 41A05 41A10 47A30 47A63 65D05 
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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Basic SciencesPrincess Sumaya University For TechnologyAmmanJordan

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