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

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

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

In this paper, we prove the equivalence of convergence between the Mann–Ishikawa– Noor and multistep iterations for Φ− strongly pseudocontractive and Φ− strongly accretive type operators in an arbitrary Banach spaces. Results proved in this paper represent an extension and refinement of the previously known results in this area. Mathematics subject classification (2010): 47H09, 47H10, 47H15.

On the Convergence of Mann and Ishikawa Iterative Processes for Asymptotically φ-Strongly Pseudocontractive Mappings

and Applied Analysis 3 proving: 1 a fixed point theorem for an asymptotically pseudocontractive mapping that is also uniformly L-Lipschitzian and uniformly asymptotically regular, 2 that the set of fixed points of T is closed and convex, and 3 the strong convergence of a CQ-iterative method. The literature on asymptotical-type mappings is very wide see, 7–15 . In 1967, Browder 16 and Kato 17 , ...

Strong convergence of approximated iterations for asymptotically pseudocontractive mappings

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotically pseudocontractive mappings. In the present...

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...