The sufficient and necessary condition of iterative approximation to the fixed points of uniformly L-Lipschitzian asymptotically Φ-hemi-contractive mappings.

The problem of iterative approximation to the fixed points of uniformly L-Lipschitzian asymptotically Φ-hemi-contractive mappings are discussed in arbitrary Banach space. By using corresponding inequality of uniformly L-Lipschitzian and new analysis methods,a sufficient and necessary condition of modified Ishikawa iterative sequence with error approximation asymptotically Φ-hemi-contractive mappings is obtained,and some related conclusions are improved and generalized. [ABSTRACT FROM AUTHOR]