E-raamat: Convex Analysis

Krantz presents students, academics, and mathematicians with a comprehensive examination of the analytical tools of convexity and its applications in mathematics. The author has organized his text in seven segments, covering the basic ideas of convexity, its functions and applications, sophisticated ideas in convexity, and the MiniMax Theorem. The author employs a user-friendly approach throughout, with several examples and figures, illustrating the ideas he is attempting to convey. The text includes an appendices devoted to key terms, notation, and technical tools. Steven G. Krantz is a faculty member of Washington University, Missouri. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com) Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and other parts of mathematics.Convex Analysis introduces analytic tools for studying convexity and provides analytical applications of the concept. The book includes a general background on classical geometric theory which allows readers to obtain a glimpse of how modern mathematics is developed and how geometric ideas may be studied analytically. Featuring a user-friendly approach, the book contains copious examples and plenty of figures to illustrate the ideas presented. It also includes an appendix with the technical tools needed to understand certain arguments in the book, a tale of notation, and a thorough glossary to help readers with unfamiliar terms. This book is a definitive introductory text to the concept of convexity in the context of mathematical analysis and a suitable resource for students and faculty alike.