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Thorough introduction to an important area of mathematics

Contains recent results

Includes many exercises

Convex Functions and Their Applications: A Contemporary Approach

Convex Functions on Intervals.- Convex Sets in Real Linear Spaces.- Convex Functions on a Normed Linear Space.- Convexity and Majorization.- Convexity in Spaces of Matrices.- Duality and Convex Optimization.- Special Topics in Majorization Theory.- A. Generalized Convexity on Intervals.- B. Background on Convex Sets.- C. Elementary Symmetric Functions.- D. Second Order Differentiability of Convex Functions.- E. The Variational Approach of PDE.