TY  - BOOK
AU  - ARUTYUNOV, Aram V.
AU  - OBUKHOVSKII, Valeri
TI  - Convex and set-valued analysis: Selected Topics / 
T2  - De Gruyter Textbook
SN  - 9783110460308 
PY  - 2017///
CY  - Berlin : 
PB  - De Gruyter,  
KW  - UDJG
KW  - DE-Matematică
N1  - Frontmatter; Preface; Contents; Part I: Convex analysis; 1. Convex sets and their properties; 2. The convex hull of a set. The interior of convex sets; 3. The affine hull of sets. The relative interior of convex sets; 4. Separation theorems for convex sets; 5. Convex functions; 6. Closedness, boundedness, continuity, and Lipschitz property of convex functions; 7. Conjugate functions; 8. Support functions; 9. Differentiability of convex functions and the subdifferential; 10. Convex cones; 11. A little more about convex cones in infinite-dimensional spaces; 12. A problem of linear programming; 13. More about convex sets and convex hulls; Part II: Set-valued analysis; 14. Introduction to the theory of topological and metric spaces; 15. The Hausdorff metric and the distance between sets; 16. Some fine properties of the Hausdorff metric; 17. Set-valued maps. Upper semicontinuous and lower semicontinuous set-valued maps; 18. A base of topology of the space Hc(X); 19. Measurable set-valued maps. Measurable selections and measurable choice theorems; 20. The superposition set-valued operator; 21. The Michael theorem and continuous selections. Lipschitz selections. Single-valued approximations; 22. Special selections of set-valued maps; 23. Differential inclusions; 24. Fixed points and coincidences of maps in metric spaces; 25. Stability of coincidence points and properties of covering maps; 26. Topological degree and fixed points of set-valued maps in Banach spaces; 27. Existence results for differential inclusions via the fixed point method; Notation; Bibliography; Index
UR  - https://www-degruyter-com.am.e-nformation.ro/view/title/517815?tab_body=overview
ER  -