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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Geometric estimation of the solution to $ x+Tx=0$ for unbounded densely defined monotone operator $ T$ in Hilbert space


Author: T. E. Williamson
Journal: Proc. Amer. Math. Soc. 74 (1979), 278-284
MSC: Primary 47H15; Secondary 65J15
DOI: https://doi.org/10.1090/S0002-9939-1979-0524300-9
MathSciNet review: 524300
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Abstract: In recent papers R. Bruck and J. C. Dunn have given convergent schemes for approximating the solution p of $ x + Tx = f$ for T a monotone mapping on a Hilbert space, with T locally bounded. The present paper derives a geometric fact and uses this in a direct manner to give a scheme applicable to densely defined T. The scheme is computable with decreasing error estimates without any assumptions of boundedness. The convergence of the scheme to the solution p is proven under the weak condition that $ \left\Vert {{x_n} + T{x_n}} \right\Vert$ grow no faster than $ {n^{1/2}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0524300-9
Article copyright: © Copyright 1979 American Mathematical Society