The solution by iteration of nonlinear equations in Hilbert spaces
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- Proc. Amer. Math. Soc. 63 (1977), 69-73 Request permission
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.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- 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