The solution by iteration of nonlinear equations in Hilbert spaces

Măruşter, Şt.

doi:10.1090/S0002-9939-1977-0636944-2

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.

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