Set-Valued Analysis
Set-Valued Analysis
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DOI：
10.1007/978-1-4419-9158-4_4
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发表时间：
2021-08
期刊：
影响因子：
17.1
通讯作者：
Z. Denkowski;S. Migórski;N. Papageorgiou
中科院分区：
文献类型：
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作者：
Z. Denkowski;S. Migórski;N. Papageorgiou
“多值分析”是集值映射（称为多函数）的理论，在许多不同的领域都有重要的应用。多值分析是一门融合了点集拓扑、测度理论和非线性泛函分析等数学领域的学科。它也与“非光滑分析”（第5章）密切相关，事实上，该理论发展背后的主要动机之一是为了为研究非光滑分析中的问题提供必要的分析工具。这两个领域的发展在时间上是一致的，并遵循平行的道路，这不是巧合。今天，多值分析是一个成熟的数学领域，有自己的方法、技术和应用，从社会科学和经济科学到生物科学和工程。毫无疑问，一篇关于“非线性泛函分析”的现代论文不能忽视多值分析。多功能理论的缺失将极大地限制其可能的应用。
“Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.