Cybernetics and Systems Analysis

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

On a theorem of M. A. Krasnoselski

Brief Communications


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.


simple iteration method convergence operator equation solvability barrelled space 


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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KievKievUkraine

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