Convex Functions and Their Applications - Constantin P. Niculescu

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Résumé :
This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics. The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples. Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-P?lya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory. This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, and it can also be used as a reference text for graduate courses on convex functions and applications....

Biographie:
Constantin P. Niculescu is professor emeritus at the University of Craiova, Romania, and a member of the Academy of Romanian Scientists. He received his Ph.D. from the University of Bucharest in 1974. He published more than one hundred papers and several books in functional analysis, operator theory, convex analysis, ergodic theory, history and heuristics of mathematics and has received several prizes both for research and exposition. Lars-Erik Persson is a Professor of Mathematics at Lule? University of Technology, Sweden, and also at UiT, The Artic University of Norway. He is honorary Professor at Eurasian National University, Kazakhstan, and he has served as President of the Swedish Mathematical Society. He received his doctorate from Ume? University in 1974. Dr. Persson has published around 300 papers on functional analysis, interpolation of operators, Fourier analysis, function theory, inequalities and homogenization theory. He has been a supervisor for 62students with PhD exams and he has received several awards both for research and teaching....

Sommaire:
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.