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Cybernetics and Systems Analysis

, Volume 46, Issue 6, pp 1021–1024 | Cite as

On a theorem of M. A. Krasnoselski

  • S. I. Lyashko
  • V. V. Semenov
Brief Communications
  • 33 Downloads

Abstract

A solvability criterion is proved for a second-kind operator equation with a correct endomorphism of Hausdorff barrelled spaces. The resultant assertion is a generalization of the theorem of M. A. Krasnoselski on the convergence of the Picard iteration method for solving equations with nonexpansive self-adjoint operators.

Keywords

simple iteration method convergence operator equation solvability barrelled space 

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References

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    M. A. Krasnoselskii, “On the solution of equations with self-adjoint operators by the method of successive approximations,” Usp. Mat. Nauk, 15, No. 3, 161–165 (1960).MathSciNetGoogle Scholar
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    M. A. Krasnoselski, G. M. Vainikko, and P. P. Zabreiko, et al., Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).Google Scholar
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    S. I. Lyashko, D. A. Nomirovskii, Yu. I. Petunin, and V. V. Semenov, The 20th Hilbert Problem: Generalized Solutions of Operator Equations [in Russian], OOO “I.D. Williams,” Moscow (2009).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KievKievUkraine

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