Selections and parametrization for set-valued maps

ABSTRACT Master of Science Thesis SELECTIONS AND PARAMETRIZATION FOR SET- VALUED MAPS AYŞE FİDAN Anadolu University Graduate School of Natural And Applied Sciences Mathematics Program Supervisor: Doç. Dr. Mahide Küçük 2000, Page 70 This study is a collection study that includes the existence of continu ous and Lipschitz selections for set-valued maps and the problem of parametriza- tion for set- valued maps. This study is composed of four parts. In the first part, basic definitions and theorems and properties of convex sets and functions are given. In the second parts, the existence of continuous selections of upper and lover semicontinuous set-valued maps is searched. At the end of this part continuity property of minimal selections of set- valued maps is given. In the third part, Steiner point of convex and compact sets is defined, with the help of this definition the existence of Lipschitz selections of closed and convex valued Lipschitz set-valued maps is searched. Furthermore, existence of Caratheodory selections which is often used in control theory is proved. iiiIn the final part, two parametrizations for set-valued maps are given. Key Words: Set-Valued Maps, Upper and Lover Semicontinuity, Selections, Parametrizations. )V