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Strong convergence of an iterative method for nonexpansive and accretive operators. (English) Zbl 1086.47060
The author in this paper establishes a strong convergence result for the iteration sequence \(\{x_n\}\) defined by \[ x_{n+1}= \alpha_n u+ (1-\alpha_n) Jr_n x_n, \] where \(\alpha_n\subset(0,1)\) and \(\{r_n\}\) is a sequence of positive terms, in a closed convex subset of a reflexive Banach space with a weakly continuous duality mapping \(J_\varphi\) with gauge \(\varphi\), to a fixed point of an \(m\)-accretive operator. Similar results are also established for uniformly smooth Banach space.

MSC:
47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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References:
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