Majorization and Karamata Inequality by Pham Kim Hung, Stanford University, US

- This is an excerpt from the second volume of ”Secrets In Inequalities”, by Pham Kim Hung. The author thanks sincerely Darij Grinberg for some of his materials about Symmetric Majorization Theorem, posted on Mathlinks Forum. Please don’t use this excerpt for any commercial purpose. The Author always appriciates every Contribution to this content- Majorization and
Karamata Inequality.

• Chapter 1: Theory of Majorization
• Chapter 2: Karamata Inequality

- Using Karamata inequality together with the theory of majorization like we have just done it is an original method for algebraic inequalities. By this method, a purely algebraic problem can be transformed to a linear inequality with absolute signs, which
is essentially an arithmetic problem, and which can have many original solutions

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