The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems

Lu-ChuanCeng; HimanshuGupta; Ching-FengWen

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The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems

机译：带正则化的Mann型超梯度迭代算法，用于解决变分不等式问题，分裂可行性和不动点问题

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The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution setΞof a general system of variational inequalities, the solution setΓof a split feasibility problem, and the fixed point setFix(S)of a strictly pseudocontractive mappingSin the setting of the Hilbert spaces. These iterative algorithms are based on the regularization method, the Mann-type iteration method, and the extragradient method due to Nadezhkina and Takahashi (2006). Furthermore, we prove that the sequences generated by the proposed algorithms converge weakly to an element ofFix(S)∩Ξ∩Γunder mild conditions.

机译：本文的目的是介绍和分析带正则化的Mann型超梯度迭代算法，以找到一般变分不等式系统的解集Ξ，分裂可行性问题的解集Γ和不动点集Fix（S严格伪压缩映射）在希尔伯特空间的设置中。由于Nadezhkina和Takahashi（2006），这些迭代算法基于正则化方法，Mann型迭代方法和超梯度方法。此外，我们证明了在温和条件下，所提算法生成的序列弱收敛至Fix（S）∩Ξ∩Γ的一个元素。

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《Abstract and applied analysis》 |2013年第2期|共19页
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Lu-ChuanCeng; HimanshuGupta; Ching-FengWen;
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2. Multi-step extragradient method with regularization for triple hierarchical variational inequalities with variational inclusion and split feasibility constraints [J] . Lu-Chuan Ceng, Chin-Tzong Pang, Ching-Feng Wen Journal of inequalities and applications . 2014,第1期

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3. Simultaneous extragradient iterative method to a split equality variational inequality problem and a multiple-sets split equality fixed point problem for multi-valued demicontractive mappings [J] . Kazmi Kaleem Raza, Furkan Mohd, Ali Rehan Advances in Fixed Point Theory . 2019,第2期

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The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems

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