On a theorem of M. A. Krasnoselski
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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.
Keywordssimple iteration method convergence operator equation solvability barrelled space
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- 2.M. A. Krasnoselski, G. M. Vainikko, and P. P. Zabreiko, et al., Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).Google Scholar
- 5.Yu. M. Berezanskii, G. F. Us, and Z. G. Sheftel, Functional Analysis [in Russian], Vyshch. Shkola, Kyiv (1990).Google Scholar
- 6.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