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.
Tabella dei contenuti
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.-
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