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Viscosity approximation methods for nonexpansive semigroups in CAT(0) spaces

Research paper by Rabian Wangkeeree, Pakkapon Preechasilp

Indexed on: 19 Jun '13Published on: 19 Jun '13Published in: Fixed Point Theory and Applications



Abstract

In this paper, we study the strong convergence of Moudafi’s viscosity approximation methods for approximating a common fixed point of a one-parameter continuous semigroup of nonexpansive mappings in CAT(0)Open image in new window spaces. We prove that the proposed iterative scheme converges strongly to a common fixed point of a one-parameter continuous semigroup of nonexpansive mappings which is also a unique solution of the variational inequality. The results presented in this paper extend and enrich the existing literature.