M.Sc Thesis | |

M.Sc Student | Boulos Wissam |
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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.