In this article, we propose a viscosity extragradient algorithm together with an inertial extrapolation method for approximating the solution of pseudomonotone equilibrium and fixed point problem of a nonexpansive mapping in the setting of a Hadamard manifold. We prove that the sequence generated by our iterative method converges to a solution of the above problems under some mild conditions. Finally, we outline some implications of our results and present several numerical examples showing the implementability of our algorithm. The results of this article extend and complement many related results in linear spaces.

中文翻译：

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修正惯性法的粘度外梯度求解Hadamard流形平衡问题和不动点问题

在本文中，我们提出了一种粘性外梯度算法和惯性外推法，用于逼近阿达玛流形设置下非扩张映射的伪单调平衡和不动点问题的解。我们证明，在一些温和的条件下，迭代方法生成的序列收敛于上述问题的解。最后，我们概述了我们的结果的一些含义，并提供了几个显示我们算法的可实施性的数值示例。本文的结果扩展并补充了线性空间中的许多相关结果。