Stable iteration procedures for strong pseudocontractions and nonlinear equations involving accretive operators without Lipschitz assumption
In [J. Math. Anal. Appl. 204, No. 3, 677-692 (1996; Zbl 0882.47030)] \textit{M. O. Osilike} established several stability results for certain Mann and Ishikawa iteration procedures for fixed points of Lipschitz strong pseudocontractions and solutions of nonlinear accretive operator equations in real \(q\)-uniformly smooth Banach spaces. In the reviewing article the author studies the stability of these iteration processes for strong pseudocontractions without Lipschitz assumption in real uniformly smooth Banach spaces. As the consequence it is proved that these processes for approximating the solutions of the equations involving accretive operators without Lipschitz assumption are stable.
real \(q\)-uniformly smooth Banach spaces
scientific article; zbMATH DE number 1271509