 |
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| Volume 8, Number 1, April 2007, pp. 35-45 | ||||||||
| S. Dhompongsa, W. A. Kirk, and B. Panyanak | ||||||||
| Key words: | ||||||||
| Nonexpansive mappings, CAT(0) spaces, fixed points, set-valued mappings. | ||||||||
| Mathematices Subject Classification: Primary 47H09, 54H25. | ||||||||
|
||||||||
| Volume 8, Number 1, April 2007, pp. 35-45 | ||||||||
| S. Dhompongsa, W. A. Kirk, and B. Panyanak | ||||||||
| Key words: | ||||||||
| Nonexpansive mappings, CAT(0) spaces, fixed points, set-valued mappings. | ||||||||
| Mathematices Subject Classification: Primary 47H09, 54H25. | ||||||||
|
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| Abstract: | |||
| We extend recent homotopy results of Sims, Xu, and Yuan for set-valued maps to a CAT(0) setting. We also introduce an ultrapower approach to proving fixed point theorems for nonexpansive set-valued mappings, both in this setting and in Banach spaces. This method provides an efficient way of recovering all of the classical Banach space results. | |||
| Nonexpansive set-valued mappings in metric and Banach spaces | ||