We introduce a new algorithm (horizontal algorithm) in a real Hilbert space, for approximating a common fixed point of a finite family of mappings, without imposing on the finite family of the control sequences , the condition that , for each . Furthermore, under appropriate conditions, the horizontal algorithm converges both weakly and strongly to a common fixed point of a finite family of type-one demicontractive mappings. It is also applied to obtain some new algorithms for approximating a common solution of an equilibrium problem and the fixed point problem for a finite family of mappings. Our work is a contribution to ongoing research on iteration schemes for approximating a common solution of fixed point problems of a finite family of mappings and equilibrium problems.

中文翻译：

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逼近有限映射族的公共不动点的新迭代方案

我们引入在实际Hilbert空间一种新的算法（水平算法），用于近似有限族映射中的一个共同的固定点，而不强加在有限家庭控制序列的，条件是，对于每个。此外，在适当的条件下，水平算法会弱而强地收敛到一类非收缩映射的有限族的一个公共不动点。它还可用于获得一些新算法，用于近似有限映射族的平衡问题和不动点问题的通用解。我们的工作为正在进行的迭代方案研究做出了贡献，这些迭代方案用于逼近有限映射和平衡问题的定点问题的通用解。