Viscosity approximation methods for a family of nonexpansive mappings in CAT(0) spaces. (English) Zbl 1472.47084

Tang, Jinfang

Abstr. Appl. Anal. 2014, Article ID 389804, 9 p. (2014).

Summary: The purpose of this paper is using the viscosity approximation method to study the strong convergence problem for a family of nonexpansive mappings in CAT(0) spaces. Under suitable conditions, some strong convergence theorems for the proposed implicit and explicit iterative schemes to converge to a common fixed point of the family of nonexpansive mappings are proved which is also a unique solution of some kind of variational inequalities. The results presented in this paper extend and improve the corresponding results of some others.

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; strong convergence; nonexpansive mappings; CAT(0) spaces; implicit iterative schemes

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