The Simplest Schemes of Generalized Solution of Linear Operator Equation

  • D. A. Klyushin
  • S. I. Lyashko
  • D. A. Nomirovskii
  • Yu. I. Petunin
  • V. V. Semenov
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 55)

Abstract

The purpose of Chap. 2 is to give a natural definition of generalized solution of non-solvable linear operator equation in Banach spaces. In Sects. 2.1–2.4 two concepts of generalized solutions are proposed: strong generalized solution and weak generalized solution based on the duality. In Sect. 2.5 the theorem on existence of a weak generalized solution is proved. The relation between these two approaches is studied in Sect. 2.6 in the case of equations with linear injective operator.

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • D. A. Klyushin
    • 1
  • S. I. Lyashko
    • 1
  • D. A. Nomirovskii
    • 1
  • Yu. I. Petunin
    • 1
  • V. V. Semenov
    • 1
  1. 1.Department of CyberneticsKyiv National Taras Shevchenko UniversityKyivUkraine

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