Award Date

1-1-1996

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

Number of Pages

66

Abstract

In this thesis, the following topics will be discussed; In chapter 2, a variational principle due to I. Ekeland (EVP) will be considered which deals with minimization of functions on a complete metric space; In chapter 3, the notion of completeness of a metric space will be characterized by means of various approaches. Several different statements will be given and shown to be all equivalent. One of these will be considered separately in chapter 4; In chapter 4, a direct approach to finding a fixed point of a self-mapping T on a complete metric space will be discussed. A transfinite induction argument will be used; Chapter 5 deals with an application. We will present a new proof of a Minimum/Maximum Principle at Infinity using Ekeland's Variational Principle; Finally, in chapter 6, we will give an informal explanation (through an iteration process) of how transfinite induction works in finding fixed points of T. Several illustrative examples will be presented.

Keywords

Connection; Fixed; Point; Principle; Theory; Variational

Controlled Subject

Mathematics

File Format

pdf

File Size

1228.8 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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