ABSTRACT

The purpose of this paper is to study the method of approximation for zeros of the sum of a finite family of maximal monotone mappings in the setting of Banach spaces. Under some mild conditions, we establish strong convergence results of the proposed approximation method. The assumptions that one of the mappings is single valued and α-inverse strongly monotone are dispensed with. In addition, we give some applications to the minimization problems. Finally, we provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

中文翻译：

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Banach 空间中最大单调映射的有限族之和为零的收敛结果

摘要

本文的目的是研究在Banach空间的设置下，一个最大单调映射的有限族之和的逼近方法。在一些温和的条件下，我们建立了所提出的近似方法的强收敛结果。省略了其中一个映射是单值且α-逆强单调的假设。此外，我们给出了最小化问题的一些应用。最后，我们提供了一个支持我们主要结果的数值示例。我们的定理改进并统一了已证明的这一重要类别的非线性映射的大多数结果。