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A new efficient algorithm for finding common fixed points of multivalued demicontractive mappings and solutions of split generalized equilibrium problems in Hilbert spaces
International Journal of Computer Mathematics ( IF 1.8 ) Pub Date : 2020-12-15 , DOI: 10.1080/00207160.2020.1856823
L. O. Jolaoso 1, 2 , O. K. Oyewole 1, 2 , K. O. Aremu 1 , O. T. Mewomo 1
Affiliation  

ABSTRACT

The purpose of this article is to present a new iterative technique for approximating solutions of split generalized equilibrium problem and common fixed points of multivalued demicontractive mappings satisfying the gate conditions in real Hilbert spaces. Unlike the earlier results in this direction, we obtain a strong convergence result using an Armijo line search rule for determining the best appropriate step size for the next iteration. Also, our algorithm is designed in such a way that it does not require a projection onto the feasible set. We further give an analysis of the convergence rate of our method which is shown to be O(1/t). Finally, the performances and comparisons with some existing methods are presented through numerical experiments. This result extends, generalizes and improves many of the existing related results in a unified way.



中文翻译:

希尔伯特空间中多值解收缩映射公共不动点的一种新有效算法及分裂广义均衡问题的解

摘要

本文的目的是提出一种新的迭代技术,用于逼近分裂广义均衡问题和满足实 Hilbert 空间中门条件的多值去收缩映射的公共不动点的解。与此方向的早期结果不同,我们使用 Armijo 线搜索规则来确定下一次迭代的最佳步长,从而获得强收敛结果。此外,我们的算法是这样设计的,它不需要在可行集上进行投影。我们进一步分析了我们方法的收敛速度,结果表明(1/). 最后,通过数值实验展示了性能和与一些现有方法的比较。该结果以统一的方式扩展、概括和改进了许多现有的相关结果。

更新日期:2020-12-15
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