Convergence theorems for \(\psi\)-expansive and accretive mappings (Q860721)

The authors make use of (projection) perturbed Mann iterations in order to approximate zeros, respectively fixed points, of the mappings under consideration. Recall that, for a selfmapping \(T\) of a closed convex subset \(K\) of a normed linear space \(E\), the perturbed Mann iteration sequence is defined by \(x_1\in E\) and \[ x_{n+1}=(1-\lambda_{n}) x_{n}+\lambda_{n} T x_{n}-\lambda_{n} \theta_{n} (x_{n}-x_{1}), \,\,n \geq 1, \] where \(\{\lambda_n\}\) and \(\{\theta_n\}\) are real sequences in \((0,1]\) satisfying appropriate conditions.