In 2003, Xu [13] proved that the sequence defined by the iterative method below, with the initial guess chosen arbitrarily (16).
In [10, 11], it is proved that the sequence defined by the iterative method below, with the initial guess chosen arbitrarily, (1.10).
In[3] (see also [4]), it is proved that the sequence defined by the iterative method below, with the initial guess chosen arbitrarily, (1.3).
In this paper, motivated and inspired by Atsushiba and Takahashi [9], Lau et al. [10], Marino and Xu [6] and Xu [4, 11], we introduce the iterative below, with the initial guess chosen arbitrarily, (1.14).
In 2003, Xu ([5]) proved that the sequence {x n } defined by the iterative method below, with the initial guess x0 ∈ H chosen arbitrarily: x n + 1 = ( I - α n A ) T x n + α n u, n ≥ 0, (1.8).
In [11], it is proved that the sequence {x n } defined by the iterative method below, with the initial guess x0 ∈ H chosen arbitrarily, x n + 1 = I - α n A T x n + α n b, n ≥ 0, strongly converges to the unique solution of the minimization problem (1.2) provided the sequence {α n } satisfies certain conditions.
In 2000, Moudafi [18] introduced the viscosity approximation method for nonexpansive mapping and proved that if H is a real Hilbert space, the sequence {x n } defined by the iterative method below, with the initial guess x0 ∈ C is chosen arbitrarily, x n + 1 = α n f ( x n ) + ( 1 - α n ) S x n, n ≥ 0, (1.10,.
In 2000, Moudafi [20] introduced the viscosity approximation method for nonexpansive mapping and prove that if H is a real Hilbert space, the sequence { x n } defined by the iterative method below, with the initial guess x 0 ∈ C is chosen arbitrarily, x n + 1 = α n f ( x n ) + ( 1 − α n ) S x n, n ≥ 0, (1.8).
The sequence { x n } defined by the iterative method below, with the initial guess x 1 ∈ H, is chosen arbitrarily, { y n = T ( x n − λ n A 1 x n ), x n + 1 = y n − μ α n A 2 y n, ∀ n ≥ 0, (1.2).
In 2003, Xu[12] proved that the sequence {x n } defined by the iterative method below, with the initial guess x0∈H chosen arbitrarily x n + 1 = ( I − α n A ) T x n + α n u, ∀ n ≥ 0, Open image in new window (1.3).
