Convergence theorems of fixed points for asymptotically hemi-pseudocontractive mappings
The authors extend the concept of asymptotically pseudocontractive mapping with nonempty fixed point set by introducing a new concept: the asymptotically hemi-pseudocontractive mapping in Banach space. For finding the fixed point of a mapping \(T\), which is a uniformly \(L\)-Lipshitzian mapping and an asymptotically hemi-pseudocontractive mapping, the authors propose a modified Ishikawa and a modified Mann iteration sequences with mean errors. The main result of the paper gives sufficient and necessary conditions on the strong convergence of the proposed iterations, to a fixed point of the mapping \(T\). An application is also discussed.
asymptotically pseudocontractive mapping
asymptotically hemi-pseudocontractive mapping
scientific article; zbMATH DE number 5612870