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Strong convergence for accretive operators in Banach spaces. (English) Zbl 1164.47376

Let \(E\) be either a uniformly smooth Banach space or a reflexive Banach space which has a weakly continuous duality map and let \(A\) be an \(m\)-accretive operator in \(E\) with \(A(0)\neq\emptyset\). Improving and extending several recent results in the literature, the authors define a composite process \(\{x_n\}_{n=1}^\infty\) and give conditions for the strong convergence of \(\{x_n\}_{n=1}^\infty\) to a zero point of \(A\).

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
54H25 Fixed-point and coincidence theorems (topological aspects)
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