We focus on two alternating inertial projection iterative algorithms to a class of split common null point problem, specifically, the common solution of the pseudomonotone variational inequality problem and the fixed-point problem of demi-contractive mapping. We construct the relation between the inertial parameters and Mann’s iteration coefficients to obtain the convergence, which in turn allows some interesting results, that is, the traditional constraints on inertia parameters can be removed. Meanwhile, we give two numerical examples to verify the superiority and effectiveness of the schemes.

The purpose of this paper is to propose a new alternative step size algorithm without using projections and without prior knowledge of operator norms to the split equality fixed point problem for a class of quasi-pseudo-contractive mappings. Under appropriate conditions, weak and strong convergence theorems for the presented algorithms are obtained, respectively. Furthermore, the algorithm proposed in this paper is also applied to approximate the solution of the split equality equilibrium and split equality inclusion problems.

采用经典的最速下降法构造一类Lipschitz连续的拟反向强单调算子的零点,在相当宽松柔和的条件下,建立了一个弱收敛结果.将弱收敛定理应用于分裂公共不动点问题,所得结果改进了近期文献的相应结果.

In this paper, we prove strong convergence theorems of Halpern's iteration for an important class of quasi-nonexpansive mappings under three different conditions on the Banach space, either reflexive with weakly sequentially continuous duality mapping or a reflexive and strictly convex one with uniformly Gateaux differentiable norm, or a uniformly smooth strictly convex one. The main results are improvement and extension of some other published results by removing some assumptions.

The purpose of this article is to propose three new hybrid projection methods for a finite family of quasi-asymptotically pseudocontractive mappings. The strong convergence of the algorithms is proved in real Hilbert spaces. Some numerical experiments are also included to compare and explain the effectiveness of the proposed methods.

. The purpose of this paper is to propose three new hybrid projection methods for a finite family of quasi-nonexpansive mappings. The strong convergence of the algorithms is proved in real Hilbert spaces. Some numerical experiments are also provided to compare and illustrate the effectiveness of the proposed algorithm.

In this paper, we improve the convergence theorem in the paper by Yang (Journal of Industrial and Management Optimization 1, 211–217, 2005), and propose a new modified convergence theorem. The theorem and the proof presented in the present paper are interesting improvements on the convergence theorem of Yang.

In this paper,we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonspreading mappings in a real Hilbert space.We obtain a strong convergence theorem for the sequences generated by this iterative scheme.

该文的目的是研究带约束的分裂公共不动点问题.建立和分析了求解带约束的分裂公共不动点问题的三种新的迭代算法.建立了三种迭代算法的强收敛性结果,这些结果改进并推广了某些作者的相关结论.

In the present paper, we propose three kinds of new algorithms for a finite family of quasi-asymptotically pseudocontractive mappings in real Hilbert spaces. By using some new analysis techniques, we prove the strong convergence of the proposed algorithms. Some numerical examples are also included to illustrate the effectiveness of the proposed algorithms. The results presented in this paper are interesting extensions of those well-known results.

In this paper ,a perturbed Krasnosel’skii‐Mann iterative algorithm is introduced ,and the con‐vergence of the proposed algorithm is established for nonexpansive mappings in Banach spaces .This result improves and generalizes a weak convergence theorem due to Reich .As an application the split feasibility problem is solved .

In this paper, we present several remarks on the paper by Yao et al. (citeyearcite.nine). The results presented in the present paper are interesting improvements on the main results of Yao et al.

针对一类单调型变分不等式,引入一种新的迭代算法,证明所引入的算法强收敛性,所得结果拓展了已有的相关结论.

给出了Banach空间中拟φ-渐近非扩张映像族公共不动点的一个修正的迭代算法,并利用所给出的算法证明了一个强收敛定理.

针对Hilbert空间中拟非扩张非自映像引入了三种新的粘滞方法,并证明了所提出的三种算法的强收敛,改进和推广了相关的结果.

In this paper, we provide a more general regularization method for seeking a solution to a class of monotone variational inequalities in a real Hilbert space, where the regularizer is a hemicontinuous and strongly monotone operator. As a discretization of the regularization method, we propose an iterative method. We then prove that the proposed iterative method converges in norm to a solution of the class of monotone variational inequalities. We also apply our results to the constrained minimization problem and the minimum-norm fixed point problem for a generalized Lipschitz continuous and pseudocontractive mapping. The results presented in the paper improve and extend recent ones in the literature.

The purpose of this paper is to present two new iterative algorithms to find the minimum norm fixed point of nonexpansive nonself-mappings in the framework of Hilbert spaces. The results presented in this paper improve and extend the corresponding ones announced by Yao and Xu [Yao Y, Xu HK. Iterative methods for finding minimum norm fixed point of mappings with applications. Optimization. 2011;60:645-658] and many others. Some applications to convex minimization and split feast problems(SFP) are also included.

In this paper, we introduce two kinds of iterative methods for finding the minimum-norm solution to the standard monotone variational inequality problems in a real Hilbert space. We then prove that the proposed iterative methods converge strongly to the minimum-norm solution of the variational inequality. Finally, we apply our results to the constrained minimization problem and the split feasibility problem as well as the minimum-norm fixed point problem for pseudocontractive mappings.

A new iterative algorithm is introduced to construct fixed points for Lipschitz pseudo‐con‐tractive mappings in Hilbert spaces .The algorithm is proved to be strongly convergent ,in particular ,a method for minimum‐norm fixed point of Lipschitz pseudo‐contractive mappings is obtained .