通过定向距离函数实现平衡问题解映射的豪斯多夫连续性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-27 DOI:10.1007/s11590-024-02098-w

Lam Quoc Anh, Nguyen Huu Danh, Pham Thanh Duoc

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引用次数: 0

摘要

本文旨在研究平衡问题解映射在豪斯多夫连续性意义上的稳定性，而不假定有序锥体的实体条件。我们首先提出了集值映射的广义凹性，并讨论了它与现有概念的关系。然后，利用上述性质和目标函数的连续性，建立了标量平衡问题解映射的豪斯多夫连续性的充分条件。最后，我们利用定向距离函数，通过标量均衡问题的相应结果，得到了集值均衡问题解映射的 Hausdorff 连续性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hausdorff continuity of solution maps to equilibrium problems via the oriented distance function

This paper aims to study the stability in the sense of Hausdorff continuity of solution maps to equilibrium problems without assuming the solid condition of ordered cones. We first propose a generalized concavity of set-valued maps and discuss its relation with the existing concepts. Then, by using the above property and the continuity of the objective function, sufficient conditions for the Hausdorff continuity of solution maps to scalar equilibrium problems are established. Finally, we utilize the oriented distance function to obtain the Hausdorff continuity of solution maps to set-valued equilibrium problems via the corresponding results of the scalar equilibrium problems.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.