Sentence examples for by the viscosity approximation from inspiring English sources

Recently, Takahashi and Takahashi in [19] first introduced an iterative scheme by the viscosity approximation method.

Subsequently, Ceng and Yao [13] introduced an iterative scheme by the viscosity approximation method: (1.8).

In this paper, motivated by above-mentioned results, we introduce a new composite iterative scheme by the viscosity approximation method.

Recently, Marino and Xu [8] introduced a new iterative scheme by the viscosity approximation method [12]: (1.11).

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings and monotone mappings in a Hilbert space.

Recently, Marino and Xu [3] introduced a new iterative scheme from an arbitrary point by the viscosity approximation method as follows: (1.7).

In 2008, Yao et al. [8] modified Mann's iterative scheme by using the viscosity approximation method which was introduced by Moudafi [1].

Q is sunny and nonexpansive; ∥ Q x − Q y ∥ 2 ≤ 〈 x − y, j ( Q x − Q y ) 〉, ∀ x, y ∈ E ; 〈 x − Q x, j ( y − Q x ) 〉 ≤ 0, ∀ x ∈ E, y ∈ C. Recently, Xu [6] improved Reich's results by considering the viscosity approximation method which was first introduced by Moudafi [7].

The purpose of this paper is by using the viscosity approximation method to study the strong convergence problem for two one-parameter continuous semigroups of nonexpansive mappings in CAT 0) spaces.

Recently by using the viscosity approximation method S. Takahashi and W. Takahashi [8] introduced another iterative algorithm for finding a common element of the set of solutions of (EP) and the set of fixed points of a nonexpansive mapping in a real Hilbert space.

The purpose of this paper is to introduce a new iteration by the combination of the viscosity approximation with Meir-Keeler contractions and proximal point algorithm for finding common zeros of a finite family of accretive operators in a Banach space with a uniformly Gâteaux differentiable norm.