In this paper, we combine the S-iteration process introduced by Agarwal et al. (J. Nonlinear Convex Anal., 8(1), 61–79 2007) with the proximal point algorithm introduced by Rockafellar (SIAM J. Control Optim., 14, 877–898 1976) to propose a new modified proximal point algorithm based on the S-type iteration process for approximating a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mappings in the framework of CAT(0) spaces and prove the △-convergence of the proposed algorithm for solving common minimization problem and common fixed point problem. Our result generalizes, extends and unifies the corresponding results of Dhompongsa and Panyanak (Comput. Math. Appl., 56, 2572–2579 2008), Khan and Abbas (Comput. Math. Appl., 61, 109–116 2011), Abbas et al. (Math. Comput. Modelling, 55, 1418–1427 2012) and many more.

在本文中，我们结合了Agarwal等人介绍的S迭代过程。（J.非线性凸元素分析，8（1），61-79 2007）与由Rockafellar引入的邻近点算法（SIAM J.控制的Optim。 ，14，877-898，1976），提出基于一种新的改性的邻近点算法在S上型迭代过程，用于逼近凸最小化问题解集和CAT（0）空间框架中近渐近拟非扩张映射的不动点集的一个公共元素，并证明了该算法的△收敛性用于解决常见的最小化问题和常见的定点问题。我们的结果推广，延伸，并且相结合Dhompongsa和Panyanak（的对应结果COMPUT。数学申请。，56，2572年至2579年2008年），汗和阿巴斯（COMPUT。数学申请。，61，109-116 2011），阿巴斯等。（数学COMPUT，建模，55，1418年至1427年2012）等等。