|M.Sc Student||Boulos Wissam|
|Subject||Best Approximations; Farthest Points and Porosity|
in Banach and Hyperbolic Spaces
|Department||Department of Mathematics||Supervisor||PROFESSOR EMERITUS Simeon Reich|
|Full Thesis text|
This thesis presents several generic existence theorems and propositions concerning best approximations and farthest point problems in Banach and complete hyperbolic spaces using the notion of porosity.
In Chapter 1 of the thesis we define the notion of porosity and discuss a few of its properties. Chapter 2 contains a survey of results for best approximation problems. In Chapter 3 we prove a farthest point theorem in complete hyperbolic spaces. Chapter 4 deals with a correction to the proof of a certain best approximation result in Banach spaces. In Chapter 5 we prove a best approximation result and a farthest point result in complete hyperbolic spaces. Chapter 6 gives a survey of theorems and propositions for farthest point problems in Banach spaces. In Chapter 7 we prove a geometry dependent farthest point theorem.