Mann and Ishikawa iteration schemes for multivalued mappings in CAT(0) spaces. (English) Zbl 1231.47068

Puttasontiphot, Tippawan

Appl. Math. Sci., Ruse 4, No. 61-64, 3005-3018 (2010).

The author proves strong convergence theorems for the Mann and Ishikawa iteration schemes involving quasi-nonexpansive multivalued mappings in the framework of CAT(0) spaces. These results are analogs of some results given by N. Shahzad and H. Zegeye [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 3–4, A, 838–844 (2009; Zbl 1218.47118)] for the case of Banach spaces.

Reviewer: Ioan A. Rus (Cluj-Napoca)

MSC:

47J25	Iterative procedures involving nonlinear operators
54H25	Fixed-point and coincidence theorems (topological aspects)
54E40	Special maps on metric spaces

Keywords:

CAT(0) space; multivalued mapping; fixed point; Mann iteration; Ishikawa iteration; strong convergence

Citations:

Zbl 1218.47118