Applications in Fixed Point Theory

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.

Grantor dc:publisher

University of North Texas

Year dc:date

2005

Author dc:creator

• Farmer, Matthew Ray

Contributors dc:contributor

• Bator, Elizabeth M.
• Lewis, Paul
• Jackson, Stephen C.

• Fixed point theory.
• Banach spaces.
• metric space
• non-expansive maps
• contraction maps
• fixed points
• Hilbert spaces

Statement dc:rights

• Public
• Copyright
• Farmer, Matthew Ray
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 68903182
https://digital.library.unt.edu/ark:/67531/metadc4971/
ark: ark:/67531/metadc4971

OAI identifier oai:identifier

info:ark/67531/metadc4971