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Fixed point theorems in spaces and -trees


We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.

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Correspondence to WA Kirk.

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Kirk, W. Fixed point theorems in spaces and -trees. Fixed Point Theory Appl 2004, 738084 (2004).

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