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Springer Optimization and Its Applications
cover

Generalized Solutions of Operator Equations and Extreme Elements

Authors: Klyushin, D.A., Lyashko, S.I., Nomirovskii, D.A., Petunin, Y.I., Semenov, V.

  • Contains recently obtained results in linear operator theory with applications to optimal control theory
  • Provides new methods of identifying solutions of linear and nonlinear operator equations
  • Can serve as a text in graduate courses and seminars in functional analysis and optimal control theory
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About this book

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.

Reviews

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. Zabreĭko, 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)


Table of contents (8 chapters)

Table of contents (8 chapters)
  • The Major Definitions, Concepts and Auxiliary Facts

    Pages 1-5

    Klyushin, D. A. (et al.)

  • The Simplest Schemes of Generalized Solution of Linear Operator Equation

    Pages 7-15

    Klyushin, D. A. (et al.)

  • A Priori Estimates for Linear Continuous Operators

    Pages 17-27

    Klyushin, D. A. (et al.)

  • Applications of the Theory of Generalized Solvability of Linear Equations

    Pages 29-101

    Klyushin, D. A. (et al.)

  • Computation of Near-Solutions of Operator Equations

    Pages 103-124

    Klyushin, D. A. (et al.)

Buy this book

eBook 96,29 €
price for Spain (gross)
  • ISBN 978-1-4614-0619-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-1-4614-0618-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-1-4614-2964-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Generalized Solutions of Operator Equations and Extreme Elements
Authors
Series Title
Springer Optimization and Its Applications
Series Volume
55
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media LLC
eBook ISBN
978-1-4614-0619-8
DOI
10.1007/978-1-4614-0619-8
Hardcover ISBN
978-1-4614-0618-1
Softcover ISBN
978-1-4614-2964-7
Series ISSN
1931-6828
Edition Number
1
Number of Pages
XXII, 202
Topics

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