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The Mann process for perturbed \(m\)-accretive operators in Banach spaces. (English) Zbl 0997.47042

The authors study the convergence of the Mann and Ishikawa iterative processes to the unique solution of \(x\) the nonlinear equation \[ z\in Sx+\lambda Ax,\quad x\in D(A),\quad z\in X,\quad \lambda>0 \] where\(A:D(A)\subseteq X\to 2^X\) is \(m\)-accretive and \(S:X\to X\) is continuous and \(\alpha\)-strongly accretive.

MSC:

47H06 Nonlinear accretive operators, dissipative operators, etc.
47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
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