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Proceedings of the American Mathematical Society

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

 

 

The solution by iteration of nonlinear equations in Hilbert spaces


Author: Şt. Măruşter
Journal: Proc. Amer. Math. Soc. 63 (1977), 69-73
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1977-0636944-2
MathSciNet review: 0636944
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Abstract: The weak and strong convergence of the iterates generated by $ {x_{k + 1}} = (1 - {t_k}){x_k} + {t_k}T{x_k}({t_k} \in R)$ to a fixed point of the mapping $ T:C \to C$ are investigated, where C is a closed convex subset of a real Hilbert space. The basic assumptions are that T has at least one fixed point in C, and that $ I - T$ is demiclosed at 0 and satisfies a certain condition of monotony. Some applications are given.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0636944-2
Keywords: Iteration, fixed points, demiclosed mappings, monotone mappings
Article copyright: © Copyright 1977 American Mathematical Society