Fixed Point Theorems in Cat ( 0 ) Spaces and R-trees

@inproceedings{Kirk2004FixedPT,
  title={Fixed Point Theorems in Cat ( 0 ) Spaces and R-trees},
  author={W. A. Kirk},
  year={2004}
}
We show that if U is a bounded open set in a complete CAT(0) spaceX , and if f : U → X is nonexpansive, then f always has a fixed point if there exists p ∈U such that x / ∈ [p, f (x)) for all x ∈ ∂U . It is also shown that if K is a geodesically bounded closed convex subset of a complete R-tree with int(K) = ∅, and if f : K → X is a continuous mapping for which x / ∈ [p, f (x)) for some p ∈ int(K) and all x ∈ ∂K , then f has a fixed point. It is also noted that a geodesically bounded complete R… CONTINUE READING

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 38 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 11 references

Fixed point theorems in R-trees with applications to graph theory, preprint

R. Espı́nola, W. A. Kirk
2004
View 1 Excerpt

Continuation results for mappings of contractive type

R. Precup
Semin. Fixed Point Theory Cluj-Napoca 2 • 2001
View 1 Excerpt

Metric Spaces of Non-Positive Curvature

M. R. Bridson, A. Haefliger
Grundlehren der Mathematischen Wissenschaften, vol. 319, Springer-Verlag, Berlin • 1999
View 3 Excerpts

Metric Structures for Riemannian and Non-Riemannian Spaces

M. Gromov
Progress in Mathematics, vol. 152, Birkhäuser Boston, Massachusetts • 1999
View 3 Excerpts

Continuation method for contractive maps

A. Granas
Topol. Methods Nonlinear Anal. 3 • 1994

Buildings

K. S. Brown
Springer-Verlag, New York • 1989
View 1 Excerpt

Uniform Convexity

K. Goebel, S. Reich
Hyperbolic Geometry, and Nonexpansive Mappings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 83, Marcel Dekker, New York • 1984
View 1 Excerpt

Continuation results for mappings of contractive type , Semin

Precup
J . Graph Theory • 1979

Fixed-edge theorem for graphs with loops

Journal of Graph Theory • 1979
View 2 Excerpts

Semi-groups of nonlinear contractions and dissipative sets

M. G. Crandall, A. Pazy
J. Functional Analysis 3 • 1969

Similar Papers

Loading similar papers…