An affirmative answer to Panyanak and Suantai’s open question on the viscosity approximation methods for a nonexpansive multi-valued mapping in CAT(0) spaces. (English) Zbl 1412.47055
Summary: An affirmative answer to the open question raised by B. Panyanak and S. Suantai [Fixed Point Theory Appl. 2015, Paper No. 114, 14 p. (2015; Zbl 1443.47073)] is given. Our results also generalize the results of Panyanak and Suantai [loc.cit.], R. Wangkeeree and P. Preechasilp [J. Inequal. Appl. 2013, Paper No. 93, 15 p. (2013; Zbl 1292.47056)], S. Dhompongsa et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 2, 459–468 (2012; Zbl 1443.47062)], and many others. Some related results in R-trees are also proved.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
viscosity approximation method; fixed point; strong convergence; multivalued nonexpansive mapping; CAT(0) spaceReferences:
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