Del 55 i serien Springer Optimization and Its Applications

Generalized Solutions of Operator Equations and Extreme Elements

Häftad, Engelska, 2013

AvD.A. Klyushin,S.I. Lyashko,D.A. Nomirovskii,Yu.I. Petunin,Vladimir Semenov

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Abstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. "Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.

Produktinformation

Utgivningsdatum2013-11-28
Mått155 x 235 x 13 mm
Vikt347 g
FormatHäftad
SpråkEngelska
SerieSpringer Optimization and Its Applications
Antal sidor202
Upplaga2012
FörlagSpringer-Verlag New York Inc.
ISBN9781461429647

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Preface.- 1. Fundamental notions, general and auxiliary facts.- 2. Simplest schemes of generalized solution of linear operator equations.- 3. A priori estimations for linear continuous operator.- 4. Applications of the theory of generalized solvability of linear equations.- 5. Scheme of generalized solutions of linear operator equations.- 6. Scheme of generalized solutions of nonlinear operator equations.- 7. Generalized extreme elements.- Reference.-

From the reviews: "This monograph principally deals with a unified approach to the notion of generalized solutions for linear and nonlinear operator equations between Banach spaces X and Y and, to a smaller degree, to the notion of generalized solutions to extremal problems for real functions defined on a set M of a Banach space. ... this book is written sufficiently well and is easy readable. Undoubtedly, it will be interesting for all specialists in Functional Analysis and Partial Differential Equations." (P. P. Zabreiko, Mathematical Reviews, Issue 2012 j) "This is a well-written, self-contained and easily readable monograph, with a reasonable number of references to English written papers and books. It can be recommended to everyone interested in the topic and having some background in functional analysis and topology." (Robert Plato, Zentralblatt MATH, Vol. 1240, 2012)