Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

We proved that the modified implicit Mann iteration process can be applied to approximate the fixed point of strictly hemicontractive mappings in smooth Banach spaces.

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science For Girls, King Abdulaziz University, Jeddah, 21593, Saudi Arabia Full list of author information is available at the end of the article Abstract Let (X ,‖ · ‖) be a Banach space. Let C be a nonempty, bounded, closed, and convex subset of X and T : C→ C be a monotone nonexpansive mapping. In this paper, it is ...

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically Φ-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically Φpseudocontractive mappings in real Banach spaces. Finally, we o...

The purpose of this paper is to prove that the modified Mann iteration process can be applied to approximate the common fixed point of three strictly hemicontractive mappings in smooth Banach spaces.