Convex and Set Valued Analysis is popular PDF and ePub book, written by Aram V. Arutyunov in 2016-12-05, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Convex and Set Valued Analysis can be Read Online from any device for your convenience.
Convex and Set Valued Analysis Book PDF Summary
This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions and their differentiability, properties of convex cones in finite- and infinite-dimensional spaces are discussed. The second part covers some important parts of set-valued analysis. There the properties of the Hausdorff metric and various continuity concepts of set-valued maps are considered. The great attention is paid also to measurable set-valued functions, continuous, Lipschitz and some special types of selections, fixed point and coincidence theorems, covering set-valued maps, topological degree theory and differential inclusions. Contents: Preface Part I: Convex analysis Convex sets and their properties The convex hull of a set. The interior of convex sets The affine hull of sets. The relative interior of convex sets Separation theorems for convex sets Convex functions Closedness, boundedness, continuity, and Lipschitz property of convex functions Conjugate functions Support functions Differentiability of convex functions and the subdifferential Convex cones A little more about convex cones in infinite-dimensional spaces A problem of linear programming More about convex sets and convex hulls Part II: Set-valued analysis Introduction to the theory of topological and metric spaces The Hausdorff metric and the distance between sets Some fine properties of the Hausdorff metric Set-valued maps. Upper semicontinuous and lower semicontinuous set-valued maps A base of topology of the spaceHc(X) Measurable set-valued maps. Measurable selections and measurable choice theorems The superposition set-valued operator The Michael theorem and continuous selections. Lipschitz selections. Single-valued approximations Special selections of set-valued maps Differential inclusions Fixed points and coincidences of maps in metric spaces Stability of coincidence points and properties of covering maps Topological degree and fixed points of set-valued maps in Banach spaces Existence results for differential inclusions via the fixed point method Notation Bibliography Index
Detail Book of Convex and Set Valued Analysis PDF
- Author : Aram V. Arutyunov
- Release : 05 December 2016
- Publisher : Walter de Gruyter GmbH & Co KG
- ISBN : 9783110460414
- Genre : Mathematics
- Total Page : 244 pages
- Language : English
- PDF File Size : 8,6 Mb
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