A relaxed Picard iteration process for set-valued operators of the monotone type

Author:
J. C. Dunn

Journal:
Proc. Amer. Math. Soc. **73** (1979), 319-327

MSC:
Primary 47H10; Secondary 65J05

DOI:
https://doi.org/10.1090/S0002-9939-1979-0518512-8

MathSciNet review:
518512

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Abstract: The fixed points of set-valued operators, , satisfying a condition of the monotonicity type on convex subsets *X* of a Hilbert space are approximated by a relaxation process, , in which is a single-valued branch of *T* and the relaxation parameter is made to depend in a certain way on the prior history of the process. If is bounded on bounded subsets of *X*, then converges to 0 like . If is also continuous at and if , then . If satisfies a condition of the Lipschitz type at , then for some .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0518512-8

Keywords:
Set-valued Hilbert space operators,
fixed points,
relaxed Picard iterations,
residual-dependent step lengths,
continuity conditions and convergence rates

Article copyright:
© Copyright 1979
American Mathematical Society