- Title
- Fixed point theory in metric and normed Spaces
- Creator
- Naude, Luan
- Subject
- Metric spaces – South Africa
- Subject
- Banach spaces – South Africa
- Subject
- Mappings (Mathematics)
- Date Issued
- 2022-12
- Date
- 2022-12
- Type
- Master's theses
- Type
- text
- Identifier
- http://hdl.handle.net/10948/59898
- Identifier
- vital:62686
- Description
- In this dissertation, we present major results in the theory of fixed points in metric and normed spaces. We start with a review of the Banach fixed point theorem and some of its applications (in systems of linear equations, differential equations, integral equations, and dynamical systems), and then discuss many of its extensions and generalizations. We look at the theorem of Edelstein ([8, Remark 3.1]) in compact metric spaces, and a generalizaton of it proved by Suzuki ([19, Theorem 3]) in 2009. We then give a detailed account of the work of Meyers: In [11], Meyers proved generalizations of the Banach fixed point theorem to uniform local contractions, and, in [10], a converse to the Banach fixed point theorem. Finally, we look at some of Browder’s work in fixed point theory. In [6], he showed the existence of fixed points for nonexpansive mappings on bounded, closed, and convex sets in uniformly convex Banach spaces, and, in [5], he proved similar results in Hilbert spaces using a connection between nonexpansive mappings and monotone operators. Keywords: Fixed point, Functional analysis, Metric spaces, Banach spaces, Hilbert spaces, contractions, Banach fixed point theorem, nonexpansive mappings.
- Description
- Thesis (MSc) -- Faculty of Science, School of Computer Science, Mathematics, Physics and Statistics, 2022
- Format
- computer
- Format
- online resource
- Format
- application/pdf
- Format
- 1 online resource (113 pages)
- Format
- Publisher
- Nelson Mandela University
- Publisher
- Faculty of Science
- Language
- English
- Rights
- Nelson Mandela University
- Rights
- All Rights Reserved
- Rights
- Open Access
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NMU School of Computer Science, Mathematics, Physics and Statistics
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | Naude, L Dec 2022 (2).pdf | 844 KB | Adobe Acrobat PDF | View Details Download |