Artículo
CAT(k)-spaces, weak convergence and fixed points
Autor/es | Fernández León, Aurora
Espínola García, Rafael |
Departamento | Universidad de Sevilla. Departamento de Didáctica de las Matemáticas |
Fecha de publicación | 2009 |
Fecha de depósito | 2016-07-04 |
Publicado en |
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Resumen | In this paper we show that some of the recent results on ¯xed point for CAT(0) spaces
still hold true for CAT(1) spaces, and so for any CAT(k) space, under natural boundedness
conditions. We also introduce a new notion ... In this paper we show that some of the recent results on ¯xed point for CAT(0) spaces still hold true for CAT(1) spaces, and so for any CAT(k) space, under natural boundedness conditions. We also introduce a new notion of convergence in geodesic spaces which is related to the ¢-convergence and applied to study some aspects on the geometry of CAT(0) spaces. At this point, two recently posed questions in [12] (W.A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (12) (2008), 3689-3696) are answered in the negative. The work ¯nishes with the study of the Lif¸sic characteristic and property (P) of Lim-Xu to derive ¯xed point results for uniformly lipschitzian mappings in CAT(k) spaces. A conjecture raised in [4] (S. Dhompongsa, W.A. Kirk and B. Sims, Fixed points of uniformly lipschitzian mappings, Nonlinear Anal., 65 (2006), 762{772) on the Lif¸sic characteristic function of CAT(k) spaces is solved in the positive. |
Cita | Fernández León, A. y Espínola García, R. (2009). CAT(k)-spaces, weak convergence and fixed points. Journal of Mathematical Analysis and Applications, 363 (1), 410-427. |
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