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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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