Master of Science (MS)
Number of Pages
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.
Connection; Fixed; Point; Principle; Theory; Variational
University of Nevada, Las Vegas
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https://doi.org/10.25669/f588-rrtf processed, response: 201
Ohashi, Ryo, "A variational principle and its connection with fixed point theory" (1996). UNLV Retrospective Theses & Dissertations. 3291.