In this paper, we use the gate condition on two multivalued k-demicontractive mappings to approximate a common solution of a finite family of monotone inclusion problem and fixed point problem in CAT(0) space. Furthermore, we propose a Halpern-type proximal point algorithm and prove its strong convergence to a common solution of a finite family of monotone inclusion problems and fixed point problem for two multivalued k-demicontractive mappings in a complete CAT(0) space. We also applied our result to the problem of finding a common solution of a finite family of minimization problem and fixed point problem in CAT(0) space. Finally, numerical experiments of our result are presented to further show its applicability.

中文翻译：

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CAT（0）空间中非紧缩多值映射的单调包含有限族和不动点问题的公共解的逼近

在本文中，我们将门条件用于两个多值k-减缩映射，以逼近CAT（0）空间中单调包含问题和不动点问题的有限族的公共解。此外，我们提出了一种Halpern型近端点算法，并证明了其对于完整CAT（0）空间中两个多值k-减缩映射的单调包含问题和不动点问题的有限解的一个共同解的强收敛性。我们还将我们的结果应用于在CAT（0）空间中找到最小化问题和不动点问题的有限族的公共解的问题。最后，对我们的结果进行了数值实验，以进一步证明其适用性。