Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841613 | Nonlinear Analysis: Theory, Methods & Applications | 2010 | 10 Pages |
Abstract
Very recently, Yao, Chen and Yao [20] proposed a hybrid viscosity approximation method, which combines the viscosity approximation method and the Mann iteration method. Under the convergence of one parameter sequence to zero, they derived a strong convergence theorem in a uniformly smooth Banach space. In this paper, under the convergence of no parameter sequence to zero, we prove the strong convergence of the sequence generated by their method to a fixed point of a nonexpansive mapping, which solves a variational inequality. An appropriate example such that all conditions of this result are satisfied and their condition βnâ0 is not satisfied is provided. Furthermore, we also give a weak convergence theorem for their method involving a nonexpansive mapping in a Hilbert space.
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Authors
Lu-Chuan Ceng, Jen-Chih Yao,