The main purpose of this paper is to introduce a new general-type proximal point algorithm for finding a common element of the set of solutions of monotone inclusion problem, the set of minimizers of a convex function, and the set of solutions of fixed point problem with composite operators: the composition of quasi-nonexpansive and firmly nonexpansive mappings in real Hilbert spaces. We prove that the sequence x n which is generated by the proposed iterative algorithm converges strongly to a common element of the three sets above without commuting assumption on the mappings. Finally, applications of our theorems to find a common solution of some nonlinear problems, namely, composite minimization problems, convex optimization problems, and fixed point problems, are given to validate our new findings.

中文翻译：

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用复合算子求解包含和不动点问题的通用型近点算法

本文的主要目的是介绍一种新的通用型近点算法，用于寻找单调包含问题的解集、凸函数的极小值集和不动点问题的解集的公共元素。使用复合算子：实 Hilbert 空间中拟非膨胀和坚定非膨胀映射的组合。我们证明了由所提出的迭代算法生成的序列 xn 强烈收敛到上述三个集合的公共元素，而无需对映射进行交换假设。最后，将我们的定理应用于寻找一些非线性问题的通用解，即复合最小化问题、凸优化问题和不动点问题，以验证我们的新发现。