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SET-Valued Analysis

In: An Introduction to Nonlinear Analysis: Theory

Author

Listed:
  • Zdzisław Denkowski

    (Jagiellonian University, Faculty of Mathematics, Physics and Computer Science Institute of Computer Science)

  • Stanisław Migórski

    (Jagiellonian University, Faculty of Mathematics, Physics and Computer Science Institute of Computer Science)

  • Nikolas S. Papageorgiou

    (National Technical University, Department of Mathematics)

Abstract

“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.

Suggested Citation

  • Zdzisław Denkowski & Stanisław Migórski & Nikolas S. Papageorgiou, 2003. "SET-Valued Analysis," Springer Books, in: An Introduction to Nonlinear Analysis: Theory, chapter 0, pages 405-516, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9158-4_4
    DOI: 10.1007/978-1-4419-9158-4_4
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