Applications in Fixed Point Theory

Description:

Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.

Creator(s): Farmer, Matthew Ray
Creation Date: December 2005
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
Usage:
Total Uses: 735
Past 30 days: 17
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Creator (Author):
Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: December 2005
  • Digitized: February 12, 2008
Description:

Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.

Degree:
Level: Master's
Discipline: Mathematics
Language(s):
Subject(s):
Keyword(s): metric space | Banach spaces | non-expansive maps | contraction maps | fixed points | uniformly convex Banach spaces
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 68903182 |
  • ARK: ark:/67531/metadc4971
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
License: Copyright
Holder: Farmer, Matthew Ray
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.