Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings
Let \(T\) be a Lipschitzian and strongly accretive operator in \(E=L_p\), \(p\geq 2\) and \(Sx=f-Tx+x\). It is proved that under suitable conditions on the real sequences \(\{a_n\}\), \(\{b_n\}\) the iteration process \(x_0\in E\), \(x_{n+1}=(1-a_n)x_n+a_nS((1-b_n)x_n+b_nSx_n)\) converges strongly to the unique solution of \(Tx=f\).
Lipschitzian and strongly accretive operator
scientific article; zbMATH DE number 811159