Convex Functions and Their Applications

Constantin P. Niculescu is Professor Emeritus of Mathematics at the University of Craiova, Romania, and an honorary member of the "Simion Stoilow" Institute of Mathematics of the Romanian Academy.His research interests include convex analysis, functional analysis, real analysis, history, and heuristics of mathematics. He has authored several books and more than one hundred papers, for which he has been awarded several prizes for research and exposition.Lars-Erik Persson  is Professor of Mathematics  at UiT, The Arctic University of Norway, Senior Professor at Karlstad University, Sweden, and Professor Emeritus at Uppsala University, Sweden. He has been the President of the Swedish Mathematical Society  His research interests include convex analysis, functional analysis, interpolation theory, Fourier analysis, inequalities and homogenization theory  He has authored several books and around 250 papers. He has received several awards for research but also for supervision and teaching.

• Convex Functions at a First Glance.- More on Convex Functions on Intervals.- Convex Sets in Real Linear Spaces.- Convex Functions on a Normed Linear Space.- Differentiable Convex Functions. 6. Convexity and Majorization.- Convexity in Spaces of Matrices.- Convexity in Spaces of Matrices.- Duality and Convex Optimization.- Special Topics in Majorization Theory. Appendices.- Generalized Convexity on Intervals.-  Background on Convex Sets.-  Elementary Symmetric Functions.-  Second Order Differentiability of Convex Functions.-  The Variational Approach of PDE.