Set-valued analysis

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Aubin J.-P., Frankowska H.

Set-valued analysis has increasingly become recognized as an essential mathematical tool in the solution of problems arising in a diverse group of scientific, technical and other academic disciplines. Set-Valued Analysis provides, for the first time, a clear introduction to these new versatile and powerful concepts, placing them firmly in the familiar context of classical analysis, and preparing the reader to utilize directly their unifying and compelling properties.

Nonlinear analysis, nonlinear programming, mathematical economics and management, control theory, biology, systems sciences, artificial intelligence, and many other fields of investigation are rich sources of problems of a set-valued character. The models arising from these problems may lack existence and/or uniqueness in their solutions; further constraints may destroy the familiar regularity requirements; some information on the solution may be known and the coefficients unknown (inverse problems); qualitative data and/or solutions may be preferred to quantitative ones; disturbances and perturbations may have to be taken into account; plain uncertainty may be involved; and so on.

The engineer or scientist who can replace single-valued maps with set valued maps, equations with inclusions, and differential equations with differential inclusions, gains a marked advantage in the pursuit of solutions to these problems.

For graduate students and research mathematicians alike, the mathematical analysis of more and more complex systems demands the use of set-valued analysis. This broad introduction to the concepts and techniques of set-valued analysis represents a significant advance toward filling that need.

Hardcover: 488 pages

Publisher: Birkhäuser Boston; 1 edition (January 1, 1990)

Language: English

ISBN-10: 0817634789

ISBN-13: 978-0817634780

Product Dimensions: 9.1 x 6.2 x 0.8 inches

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