Abstract

In this paper, a new system of variational inclusions involving set-valued quasi-contractive, lower semi-continuous mappings with nonempty closed and convex values is introduced and studied in real Banach spaces. First, both the existence of fixed points of the set-valued quasi-contractive mappings and the solution of the system of variational inclusions are proved. Then, using the existence result, a new iterative algorithm is constructed. And then the strong convergence of the iterative sequences is proved, and the proof is novel. Finally, a numerical example is given to demonstrate the algorithm. Our results improve and extend some known results.

中文翻译：

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涉及 Banach 空间中集值拟收缩映射的变分包含系统的迭代算法

摘要

在本文中，在实巴拿赫空间中引入并研究了一种新的变分包含系统，该系统涉及具有非空闭和凸值的集合值准收缩、下半连续映射。首先，证明了集值拟收缩映射不动点的存在性和变分包含系统的解。然后，利用存在结果，构造新的迭代算法。然后证明了迭代序列的强收敛性，证明是新颖的。最后，给出了一个数值例子来说明该算法。我们的结果改进并扩展了一些已知的结果。