Overview

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.

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9781461406181

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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)

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