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Implicit Functions and Solution Mappings

A View from Variational Analysis

Implicit Functions and Solution Mappings by Asen L. Dontchev
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Setting up equations and solving them has long been so important that, in popular imagination, it has virtually come to describe what mathematical analysis and its applications are all about. A central issue in the subject is whether the solution to an equation involving parameters may be viewed as a function of those parameters, andif so,what propertiesthat functionmighthave.Thisisaddressedbytheclassical theory of implicit functions, which began with single real variables and progressed through multiple variables to equations in in?nite dimensions, such as equations associated with integral and differential operators. A major aim of the book is to lay out that celebrated theory in a broader way than usual, bringing to light many of its lesser known variants, for instance where standard assumptions of differentiability are relaxed. However, another major aim is to explain how the same constellation of ideas, when articulated in a suitably expanded framework, can deal successfully with many other problems than just solving equations.
Springer New York; Read online
Title: Implicit Functions and Solution Mappings
Author: Asen L. Dontchev; R. Tyrrell Rockafellar

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