Convergence theorems for multivalued \(\phi\)-hemicontractive operators and \(\phi\)-strongly accretive operators
For a multivalued \(\Phi\)--hemicontractive operator \(T: E \rightarrow 2^E\) with bounded range on a uniformly smooth Banach space it is shown that, under suitable conditions, both the Ishikawa and Mann iteration processes defined by \textit{Y. Xu} [J. Math. Anal. Appl. 224, No. 1, 91--101 (1998; Zbl 0936.47041)] converge strongly to the unique fixed point of \(T\). A related result concerns the iterative solution of a multivalued \(\Phi\)-accretive operator equation.
scientific article; zbMATH DE number 2102406