Set-Valued Analysis"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student." —The Journal of the Indian Institute of Science "The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes...results with many historical comments giving the reader a sound perspective to look at the subject...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." —Mathematical Reviews "I recommend this book as one to dig into with considerable pleasure when one already knows the subject...‘Set-Valued Analysis’ goes a long way toward providing a much needed basic resource on the subject." —Bulletin of the American Mathematical Society "This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps...The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis." —Zentralblatt Math |
From inside the book
Results 1-5 of 66
... Function Theorem 93 3.4.1 Derivatives of Single- Valued Maps 93 3.4.2 Constrained Inverse Function Theorems .... 94 3.4.3 Pointwise Stability Conditions 101 3.4.4 Local Uniqueness 103 3.5 Monotone and Maximal Monotone Maps 104 3.5.1 ...
... function from X x Y to R. We consider the family of minimization problems VyeF, V(y) := mfW(x,y) parametrized by parameters y. The function V is called the marginal (or performance or value) function. For every y G Y, let G(y) := {x€X\W ...
... functions. The crucial revolution in the history of the concept of gradients happened in the sixties when J.- J. Moreau and R. T. Rock- afellar proposed in the framework of convex analysis the notion of subdifferential of a convex function ...
... function: The tangent space to the graph of a function f at a point (x, y) of its graph is the line of slope f'(x), i.e., the graph of the linear function u h-> f'(x)u. It is possible to implement this idea for any set-valued map F ...
... function by using these epiderivatives. Since they enjoy a rich calculus, we obtain in this way many necessary ... function is differentiable in the usual way. In this framework, the Fermat Rule becomes: // a point achieves the minimum ...