- Title
- Nonlinear analysis in geodesic spaces
- Creator
- Searston, Ian J.
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2014
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- This thesis deals with nonlinear analysis in geodesic metric spaces, particularly in CAT(0) spaces. A major aim is to investigate the convex feasibility problem associated with the nonempty closed convex sets A and B. This problem is normally investigated in a Hilbert space setting, but in this work we have placed it into a CAT(0) setting. In chapter 2 we begin with metric spaces and move into geodesic metric spaces in order to obtain the structure which we will need in later chapters. In chapter 3 we introduce CAT(0) spaces and investigate their properties, especially those that we will need in chapters 5, 6 and 7. We also introduce new work - "Polarization in CAT(0) spaces". More new work occurs in Chapter 4 where we develop hyperplanes and half-spaces in a CAT(0) space setting and then prove a separation theorem in CAT(0) spaces. Chapter 5 covers fixed point theory in CAT(0) spaces. We use an appropriate notion of weak sequential convergence (introduced in chapter 3) to develop a fixed point theory for nonexpansive type mapping. In chapter 6 we prove that the project project algorithm works in CAT(0) spaces. In chapter 7 we set up a prototype for a CAT(0) space of non-constant curvature, develop its geometry and then investigate the Douglas-Rachford algorithm in this space.
- Subject
- nonlinear analysis; geodesic spaces; CAT(0) spaces
- Identifier
- http://hdl.handle.net/1959.13/1055353
- Identifier
- uon:15872
- Rights
- Copyright 2014 Ian J. Searston
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
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| View Details Download | ATTACHMENT01 | Abstract | 91 KB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Thesis | 2 MB | Adobe Acrobat PDF | View Details Download |