In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of $\operatorname{CAT}(0)$ spaces. We also prove the Δ-convergence of the proposed algorithm. We also provide an application and numerical result based on our proposed algorithm as well as the computational result by comparing our modified iteration with previously known Sahu’s modified iteration.

中文翻译：

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涉及近渐近拟非扩张映射的改进近点算法

在本文中，我们提出了一种基于Thakur迭代过程的改进的近点算法，以逼近凸最小化问题解集的公共元素和$ \ operatorname框架中两个近似渐近拟非扩张映射的不动点{CAT}（0）$个空格。我们还证明了所提出算法的Δ收敛性。通过比较修改后的迭代与先前已知的Sahu修改后的迭代，我们还提供了基于我们提出的算法的应用程序和数值结果以及计算结果。