Convex and set-valued analysis [online] : Selected Topics / Aram V. Arutyunov, Valeri Obukhovskii

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

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