In this paper, we introduce a new and efficient algorithm for finding a common element of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of inverse strongly monotone mappings in Hilbert spaces. Strong convergence of the proposed algorithm is established under standard and mild conditions in a Hilbert space. As an application, we use our algorithm for solving the common solutions to the variational inequality problem, the common minimization problem, the multiple-set split feasibility problem, the split common fixed point problem and the split common null point problem.

中文翻译：

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逆强单调映射的公共零点和广义二度映射的公共不动点的强收敛定理

在本文中，我们介绍了一种新的高效算法，用于寻找 Hilbert 空间中有限族广义二度映射的公共不动点集和有限族逆强单调映射的公共零点集的公共元素. 在希尔伯特空间中的标准和温和条件下，建立了所提出算法的强收敛性。作为一个应用，我们使用我们的算法来解决变分不等式问题、公共最小化问题、多集分割可行性问题、分割公共不动点问题和分割公共零点问题的公共解决方案。