Abstract

In this paper, we introduce a new system of variational inclusion problems called system of generalized set-valued variational inclusion problems involving $\alpha \beta -H((.,.),(.,.))$-mixed accretive mapping in q-uniformly smooth Banach spaces. By means of proximal-point mapping method, we prove the existence of solution of this system of variational inclusions. Further, we propose an iterative algorithm for finding the approximate solution of the system. Furthermore, we prove that the sequences generated by the iterative algorithm converge strongly to a solution of the system.

中文翻译：

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求解广义集值变分包含系统的H-混合增生映射和近点法

摘要

在本文中，我们引入了一个新的变分包含问题系统，称为广义集值变分包含问题系统，涉及 $\alpha \beta ——H((.,.),(.,.))$在-mixed增生映象q -uniformly光滑Banach空间的。通过近点映射方法，证明了该变分包体系统解的存在性。此外，我们提出了一种迭代算法来寻找系统的近似解。此外，我们证明了迭代算法生成的序列强烈收敛到系统的解。