A concept of convergence in geodesic spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 68, Issue 12, 2008, Pages 3689-3696

  Kirk, W A ^a   Panyanak, B ^b  

^a UNIVERSITY OF IOWA   (United States)

^b CHIANG MAI UNIVERSITY   (Thailand)

Author keywords

convergence; CAT(0) spaces; Fixed points; Weak convergence

Indexed keywords

BANACH SPACES; CONVERGENCE OF NUMERICAL METHODS; GEOMETRY; PROBLEM SOLVING; THEOREM PROVING;

CAT(0) SPACES; EUCLIDEAN PLANE; FIXED POINT THEORY;

MATRIX ALGEBRA;

EID: 42949122454     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.04.011     Document Type: Article

References (21)

1. Bridson M., and Haefliger A. Metric Spaces of Non-Positive Curvature (1999), Springer-Verlag, Berlin, Heidelberg
2. Burago D., Burago Y., and Ivanov S. A Course in Metric Geometry. Graduate Studies in Math. vol. 33 (2001), Amer. Math. Soc., Providence, RI
3. Bruck R.E. A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces. Israel J. Math. 32 (1979) 107-116
4. Dhompongsa S., Kirk W.A., and Panyanak B. Nonexpansive set-valued mappings in metric and Banach spaces. J. Nonlinear Convex Anal. 8 (2007) 35-45
5. Dhompongsa S., Kirk W.A., and Sims B. Fixed points of uniformly lipschitzian mappings. Nonlinear Anal. 65 (2006) 762-772
6. García-Falset J., Llorens-Fuster E., and Prus S. The fixed point property for mappings admitting a center. Nonlinear Anal. 66 (2007) 1257-1274
7. García-Falset J., Llorens-Fuster E., and Sims B. Fixed point theory for almost convex function. Nonlinear Anal. 32 (1998) 601-608
8. Goebel K., and Kirk W.A. Topics in Metric Fixed Point Theory (1990), Cambridge Univ. Press, Cambridge
9. Goebel K., and Reich S. Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings (1984), Marcel Dekker, Inc., New York
10. Khamsi M.A. La Propiété du point fixe dans les espaces de Banach avec base inconditionelle. Math. Ann. 277 (1987) 727-734
11. Kirk W.A. Nonexpansive mappings in metric and Banach spaces. Rend. Sem. Mat. Fis. Milano 51 (1981) 133-144
12. Kirk W.A. Geodesic geometry and fixed point theory. Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003). Colecc. Abierta vol. 64 (2003), Univ. Sevilla Secr. Publ., Seville 195-225
13. Kirk W.A., and Massa S. Remarks on asymptotic and Chebyshev centers. Houston J. Math. 16 (1990) 357-363
14. Kirk W.A., and Sims B. An ultrafilter approach to locally almost nonexpansive maps. Nonlinear Anal. 63 (2005) e1241-e1251
15. Kuczumow T. An almost convergence and its applications. Ann. Univ. Mariae Curie-Skłodowska Sect. A 32 (1978) 79-88 (1980)
16. Lim T.C. Remarks on some fixed point theorems. Proc. Amer. Math. Soc. 60 (1976) 179-182
17. Nussbaum R. Degree theory for local condensing mappings. J. Math. Anal. Appl. 37 (1972) 741-766
18. Reich S. Fixed points of condensing functions. J. Math. Anal. Appl. 41 (1973) 460-467
19. Reich S., and Shafrir I. Nonexpansive iterations in hyperbolic space. Nonlinear Anal. 15 (1990) 537-558
20. Sims B., and Xu H.K. Locally almost nonexpansive mappings. Comm. Appl. Nonlinear Anal. 8 3 (2001) 81-88
21. Sosov E.N. On analogues of weak convergence in a special metric space. Izv. Vyssh. Uchebn. Zaved. Mat. 5 (2004) 84-89 Translation in Russian Math. (Iz. VUZ) 48 (5) (2004) 79-83 (in Russian)