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The majorisation principle for convex functions
Published online by Cambridge University Press: 24 February 2022
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Given positive numbers xj, yj such that 
$\sum\limits_{i = 1}^n {{x_j}}= \sum\limits_{j = 1}^n {{y_j}} $, it can happen that 
$\sum\limits_{j = 1}^n {x_j^2}= \sum\limits_{j = 1}^n {y_j^2} $: for example, 
$({x_j}) = (7,\,3,\,2),\,({y_j}) = (6,\,5,\,1)$. However, such cases are exceptional.
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- © The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association
References
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