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Chang, Shih-sen; Yao, Jen-Chih; Wen, Ching-Feng; Wang, Lin

A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces. (English) Zbl 1478.65045

J. Inequal. Appl. 2018, Paper No. 235, 14 p. (2018).
Summary: The purpose of this article is to propose a modified viscosity implicit-type proximal point algorithm for approximating a common solution of a monotone inclusion problem and a fixed point problem for an asymptotically nonexpansive mapping in Hadamard spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved. Our results extend and complement some recent results in this direction.

Cited in 2 Documents

MSC:

65J15 Numerical solutions to equations with nonlinear operators
54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54C60 Set-valued maps in general topology

Keywords:

Hadamard space; CAT(0) space; viscosity implicit approximation methods; monotone mapping; proximal point algorithm
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