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Strong convergence of composite iterative schemes for zeros of \(m\)-accretive operators in Banach spaces. (English) Zbl 1226.47069
Summary: We introduce a new composite iterative scheme to approximate a zero of an \(m\)-accretive operator \(A\) defined on uniform smooth Banach spaces and a reflexive Banach space having a weakly continuous duality map. It is shown that the iterative process in each case converges strongly to a zero of \(A\). The results presented in this paper substantially improve and extend the results due to the first author and H.-K. Xu [Taiwanese J. Math. 11, No. 3, 661–682 (2007; Zbl 1219.47102)], T.-H. Kim and H.-K. Xu [Nonlinear Anal., Theory Methods Appl. 61, No. 1–2, A, 51–60 (2005; Zbl 1091.47055)] and H.-K. Xu [J. Math. Anal. Appl. 314, No. 2, 631–643 (2006; Zbl 1086.47060)]. Our work provides a new approach for the construction of a zero of \(m\)-accretive operators.

MSC:
47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
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