In this paper, we prove the Δ-convergence of a modified proximal point algorithm for common fixed points in a CAT(0) space for different classes of generalized nonexpansive mappings including a total asymptotically nonexpansive mapping, a multivalued mapping, and a minimizer of a convex function. The results in this paper generalize the corresponding results given by some authors. Moreover, numerical example is given to illustrate and show the Δ-convergence of the proposed algorithm for supporting our result.

中文翻译：

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CAT（0）空间中近点算法和不动点问题的Δ收敛

在本文中，我们证明了CAT（0）空间中公共不动点的改进近点算法的Δ收敛性，适用于不同类别的广义非膨胀映射，包括总渐近非膨胀映射，多值映射和a的最小化凸函数。本文的结果概括了一些作者给出的相应结果。此外，给出了数值示例，以说明和显示所提出算法的Δ收敛性以支持我们的结果。