A new iterative method based on the modi?ed proximal-point algorithm for ?nding a common null point of an in?nite family of accretive operators in Banach spaces

Sow T.M.M.

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A new iterative method based on the modi?ed proximal-point algorithm for ?nding a common null point of an in?nite family of accretive operators in Banach spaces

机译：一种基于MODI的近端点算法的一种新的迭代方法？在Banach空间中查找in的共同空点？

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In this paper, we introduce and study a new iterative method for ?nding a common null point of an in?nite family of accretive operators with a strongly accretive and Lipschitzian operator, by using the proximal-point algorithm. And also we prove that the common null point is a unique solution of variational inequality without imposing any compactness-type condition on either the operators or the space considered. Finally, some applications of the main results to equilibrium problems and ?xed point problems with an in?nite family of pseudocontractive mappings are given. The main result is a generalization and improvement of numerous well-known results in the available literature.

机译：在本文中，我们通过使用近端点算法，介绍和研究一种新的迭代方法而且我们证明了公共空调是变分不等式的独特解决方案，而不会对操作员或考虑的空间施加任何紧凑性型条件。最后，一些主要结果的应用结果对均衡问题和XED点问题进行给出了in？nite家庭的伪变性映射。主要结果是在可用文献中的许多众所周知的结果的泛化和改进。

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《Cubo : A Mathematical Journal》 |2020年第2期|共21页
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Sow T.M.M.;
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Proximal-point algorithmAccretive operatorsVariational inequalityCommon zeros..;

机译：近端点算法Accurretive Operatorsvaried InequalityCommon零..;

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1. NEW ITERATIVE METHODS FOR FINDING A COMMON ZERO OF A FINITE FAMILY OF ACCRETIVE OPERATORS IN BANACH SPACES [J] . Journal of nonlinear and convex analysis . 2020,第1期

机译：在Banach空间中查找有限族的共用零的新迭代方法
2. Strong convergence of a general iterative algorithm for a finite family of accretive operators in Banach spaces [J] . Yanlai Song, Luchuan Ceng Fixexd point theory and applications . 2015,第1期

机译：Banach空间中有限个增生算子族的通用迭代算法的强收敛性
3. Some new iterative algorithms with errors for common solutions of two finite families of accretive mappings in a Banach space [J] . Li Wei, Ruilin Tan Fixexd point theory and applications . 2014,第1期

机译：Banach空间中两个有限族增生映射的公共解的一些新的带错误的迭代算法
4. Iterative methods for solving a new system of variational inclusions with (A, η)-accretive operators in Banach spaces [C] . Jun-Min Chen, Tie-Gang Fan, Xue-Fei Li The Second International Joint Conference on Computational Science and Optimization(CSO 2009)（2009 国际计算科学与优化会议）论文集 . 2009

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5. Bases in Spaces of Regular Multilinear Operators and Homogeneous Polynomials on Banach Lattices [D] . Navoyan, Khazhak Varazdat 2018

机译：Banach格上正则多线性算子和齐次多项式空间的基
6. Strong convergence theorems for a common zero of a finite family of H-accretive operators in Banach space [O] . Huimin He, Sanyang Liu, Rudong Chen -1

机译：Banach空间中有限个H增生算子的公共零的强收敛定理
7. Strong convergence of a general iterative algorithm for a finite family of accretive operators in Banach spaces [O] . Yanlai Song, Luchuan Ceng 2015

机译：Banach空间中有限个增生算子族的通用迭代算法的强收敛性
8. Strong Convergence of Contraction Semigroups and of Iterative Methods for Accretive Operators in Banach Spaces. [R] . Nevanlinna, O., Reich, S. 1978

机译：Banach空间中增生算子的收缩半群的强收敛性及迭代算法。

A new iterative method based on the modi?ed proximal-point algorithm for ?nding a common null point of an in?nite family of accretive operators in Banach spaces

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