Applications in Fixed Point Theory

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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 ... continued below

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Farmer, Matthew Ray December 2005.

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  • Farmer, Matthew Ray

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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.

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  • December 2005

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  • Feb. 15, 2008, 4:27 p.m.

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  • Dec. 15, 2008, 2:39 p.m.

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Farmer, Matthew Ray. Applications in Fixed Point Theory, thesis, December 2005; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc4971/: accessed November 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .