The purpose of this paper is to propose and analyze a multi-step iterative sequence to solve a convex optimization problem and a fixed point problem in an Hadamard space. We aim to establish strong and \( \triangle \)-convergence results of the proposed iterative sequence by employing suitable conditions on the control parameters and the structural properties of the underlying space. As a consequence, we compute an optimal solution for a minimizer of proper convex lower semicontinuous function and a common fixed point of a finite family of total asymptotically quasi-nonexpansive mappings in Hadamard spaces. Our results can be viewed as an extension and generalization of various corresponding results in the existing literature.

中文翻译：

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Hadamard空间中定点问题和凸优化问题的多步逼近

本文的目的是提出并分析多步迭代序列，以解决Hadamard空间中的凸优化问题和不动点问题。我们的目标是通过对控制参数和底层空间的结构特性采用合适的条件，以建立拟议的迭代序列的强收敛和（三角形）收敛结果。结果，我们为Hadamard空间中适当的凸下半连续函数的极小值和有限个总渐近拟非扩张映射的有限族的公共不动点计算了一个最优解。我们的结果可以看作是现有文献中各种相应结果的扩展和概括。