On Equivalence between Convergence of Ishikawa––mann and Noor Iterations

The Equivalence among the Modified Mann–ishikawa and Noor Iterations for Uniformly L–lipschitzian Mappings in Banach Spaces

In this paper, the equivalence of the convergence among Mann-Ishikawa and Noor iterations is obtained for uniformly L-Lipschitzian mappings in real Banach spaces. Our results extend and improve the corresponding results in Chang [3] and Ofoedu [4]. Mathematics subject classification (2010): 47H10, 47H09, 46B20..

Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings

Weak and Strong Convergence Theorems for Finite Family of Nonself Asymptotically Nonexpansive Mappings in Banach Space

In this paper, several weak and strong convergence theorems are established for a new modified iterations with errors for finite family of nonself asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type and Noor-type iterations are covered by the new iteration scheme. Our convergence theorems improve, unify and generalize many important results in the current literatures.

The Equivalence of Convergence Results between Ishikawa and Mann Iterations with Errors for Uniformly Continuous Generalized Φ-Pseudocontractive Mappings in Normed Linear Spaces

We prove the equivalence of the convergence of the Mann and Ishikawa iterations with errors for uniformly continuous generalized Φ-pseudocontractive mappings in normed linear spaces. Our results extend and improve the corresponding results of Xu, 1998, Kim et al., 2009, Ofoedu, 2006, Chidume and Zegeye, 2004, Chidume, 2001, Chang et al. 2002, Liu, 1995, Hirano and huang, 2003, C. E. Chidume and...

On New Fixed-Point Iterations for Asymptotically Nonexpansive Mapping in Banach Spaces

The main purpose of this paper is to give weak and strong convergence theorems of a new three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces and we also give several weak and strong convergence theorems of the three-step iterative scheme with errors for asymptotically nonexpansive mappings in Banach spaces. Mann-type and Ishikawa -type iterations are included by...