Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups

Hongbo Liu; Yi Li

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Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups

机译：一致渐近非扩张半群有限系列的平衡问题和不动点问题的混合迭代算法收敛定理。

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Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.

机译：在整个本文中，我们引入了一种新的混合迭代算法，用于在Hilbert空间的框架中寻找一致渐近非扩张半群的有限族的公共不动点集的公共元素和平衡问题的解集。然后，我们针对所提出的迭代算法证明了强收敛定理。我们在本文中的结果扩展并改进了一些最近的已知结果。

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《Advances in Pure Mathematics》 |2014年第6期|共9页
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Hongbo Liu; Yi Li;
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中图分类数学;
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1. HYBRID ITERATION METHOD FOR GENERALIZED EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS [J] . Jinliang, Shen1, Jianhua, 应用数学年刊：英文版 . 2017,第001期

机译：渐近非扩张映象有限族的广义平衡问题与不动点问题的混合迭代法。
2. Corrigendum to: "Strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups" [Nonlinear Anal. 69 (12) (2008) 4496-4503] (DOI:10.1016/j.na.2007.11.005) [J] . Zegeye H., Shahzad N. Nonlinear Analysis: An International Multidisciplinary Journal . 2010,第6期

机译：更正为：“渐近非扩张映射和半群的有限族的强收敛定理” [非线性分析。 69（12）（2008）4496-4503]（DOI：10.1016 / j.na.2007.11.005）
3. Strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups [J] . Zegeye H, Shahzad N Nonlinear Analysis: An International Multidisciplinary Journal . 2008,第12期

机译：有限族渐近非扩张映射和半群的强收敛定理
4. Convergence Theorems of a Finite-Step Iteration Algorithm Under Two Finite Families of Total Asymptotically Quasi-Nonexpansive Maps [C] . Salwa Salman Abed, Zahra Mahmood Mohamed Hasan International Conference on Advanced Science and Engineering . 2018

机译：总渐近拟非扩张映象的两个有限族下有限步迭代算法的收敛定理
5. Fixed point and ergodic theorems for nonexpansive mappings on ultrametric Banach spaces. [D] . Farrier, Sandra N. 2005

机译：超度量Banach空间上非膨胀映射的不动点定理和遍历定理。
6. Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces [O] . Habtu Zegeye, Naseer Shahzad -1

机译：自反Banach空间中Bregman弱相对论非扩张映射的有限个族的公共不动点的强收敛定理
7. Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups [O] . Hongbo Liu, Yi Li 2014

机译：均匀渐近非派对半群有限家庭均衡问题的混合迭代算法的融合定理

Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups

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